The browser history—a list of every page you've visited online and the time you were there—is a standard of modern computing. And it can lead to trouble; it's practically a cliché. Think of the romantic "comedies" where the girl finds a guy's browser history (because it's always the guy's) and he's in scalding hot water.
For most of us, sharing a PC is normal (sadly, setting up multiple user accounts is not) and handing off a smartphone to someone isn't unheard of. It doesn't matter if you're encrypting your emails, using Tor and VPNs while browsing to stay anonymous, or if you wear a false moustache at your desk: if someone has access to your devices, they can see where you've been.
A browser can and will hold your history indefinitely. The goal is to help you find your way back to a perhaps-forgotten corner of the internet you visited once upon a time. The reality is, it can be used against you by significant others, friends, bosses, subordinates, teachers, even the authorities. It doesn't even matter if you never stopped to look at the contents; these days, simply visiting can be impetus enough for outrage, blackmail, or whatever you fear most in reprisal.
Think that's fear-mongering? Hopefully it is, for 99 percent of us. But consider that in 2016 an employee was accused of destroying evidence in a Canadian court after he cleared the browser history of his own personal laptop. (In the end, he prevailed.) In the US, the Sarbanes-Oxley Act is intended to prevent evidence deletion by corporations, yet it's been applied to at least one individual. The caveat: the individual in question also did a lot of other stupid things.
That's a very broad interpretation of Sarbanes-Oxley. Still, it's almost a guarantee that if you delete something off your drive just before you get arrested, you'll get a destruction of evidence or obstruction of justice charge, especially if the feds are involved. Apparently, people are corporations, too.
But let's assume you're not a criminal and just want a little digital privacy. What can you do to keep your past visits hidden? Delete it. Regularly. Or perhaps the smartest move of all: make sure it is never even stored. It may make your web travels a little less convenient, but that's the price of security. Here's how to remove the history.

PC Browsers

Google Chrome

Go to the three-dot menu () at the upper-right of Chrome to select Settings > Advanced > Clear browsing data or History > History > Clear browsing data. Or type "chrome://settings/clearBrowserData" in the omnibar without the quotation marks. Any of those options takes you to the dialog box to delete not only the history of your browsing, but also your download history (it won't delete the actual downloaded files), all your cookies, cached images and files (which help load pages faster when you revisit), saved passwords and more. Better yet, you can delete only the info from the last hour, day, week, month, or all of it to "the beginning of time."
Chrome - Delete Your Browser History Everywhere
Chrome doesn't give you the option to not collect your browser history, or set a window for how much it should hold. It just collects and collects until you go in and delete it.
What's more, if you have a Google account and are signed into it with Chrome, your history is likely being synced to My Activity. While it should be secured behind your Google account (use a password manager and two-factor authentication for the best protection), if you truly wish to be rid of history, go here, select the  > Web & App Activity to turn off the inclusion of Chrome browser activity (from desktops and handhelds), as well as delete any activity synced with the service.

Opera

Under the main menu in Opera, in the navigation bar on the left, click the clock icon to enter History. You'll see a Clear browsing data button that offers almost identical settings as Chrome, right down to the "beginning of time" option. (You can also type "opera://settings/clearBrowserData" into the address bar.) It's similar because Opera is built with the engine from the Chromium Project, which also underlies Chrome. Opera offers a little extra to those who want to go around the web safely however—a built-in VPN option courtesy of SurfEasy, also found in the Privacy & Security settings.
Opera browser clear data

Microsoft Edge and Internet Explorer

Go to the three-dot menu () in Microsoft Edge and select settings; in the fly-out menu, click the button under Clear browsing data that reads "Choose what to clear." Get rid of browsing history, cookies, cached data, stored form data, saved tabs, media licenses, website permissions, and stored passwords; click Manage Permissions and you can delete things like sites you've given permission to show pop-ups.
You can't delete just one chunk of data from a time period like a day or week, but there is the option to "Always clear this [data] when I close the browser." That ensures you have no browser history stored, as long as you close the browser regularly. Pick more data types and you'll have next to nothing stored—which is fine until you're entering the same passwords and 2FA logins over and over (the price of freedom, people).
Edge - Browser Clear
Like Google, Microsoft is keeping some of your history online. Click Change what Microsoft Edge knows about me in the cloud to visit a page for your Microsoft account where you can delete that synced browsing history. You can also delete search history at Bing.com, stored location data showing where you've logged in, and stuff you've stored in Cortana's notebook.
Still using Internet Explorer (IE)? You're not alone. To wipe the history in IE11 and 10, go to the Gear icon at upper left and select Internet Options. On the General tab, you can check a box next to Delete browsing history on exit, or click the Delete button to instantly get rid of history, passwords, cookies, cached data (called Temporary Internet files and website files), and more. If you instead click Settings, you go to a History tab and ensure your history is only collected for a specific number of days, automatically deleting anything older.
You have the option to get rid of your browsing history using the Favorites Menu. Click the star on the top-right > History tab. There, you can see websites you visited on specific dates (Today, Last Week, 3 Weeks Ago, etc.) Right-click to delete everything from a specific time period, or click to view and delete specific websites. If you're using an older version of IE, there are instructions online for deleting the history.

Safari

On macOS, Safari rules. Clearing your website visit history is simple: click Clear History in the History menu. Then in the pop-up, pick a timeframe for how far back you want to erase. This is doing a lot more than deleting the browser history, however—it also takes out your cookies and data cache.
You can instead click History > Show History to get a pop-up displaying every site you've visited, then take out sites individually, without losing the cookies and cache. Zap cookies by going into Preferences > Privacy; delete your cache by going to the Develop menu and picking Empty Caches. If you don't have a Develop menu in Safari, go to Preferences > Advanced and check Show Develop Menu in Menu Bar at bottom.

Mozilla Firefox

In the latest version of Firefox go to the hamburger menu () and section Options > Privacy & Security. You're instantly in the Content Blocking section; scroll down to get to History. Set Firefox to remember, to never remember, or get some custom settings like remember history, but not cookies, or whatever. This section also has a Clear History button. Click it to pick a time range to clear (1, 2, 4, or 24 hours—or everything), and what data to dump (history, logins, forms/search, cookies, and cache).
Firefox - Delete History
Check the Firefox Account section while you're in here—if you've signed on with a Mozilla Firefox account, your history (plus bookmarks, tabs, passwords, and preferences) may be synced with your other PCs and devices using Firefox, even on smartphones.

Mobile Browsers

Safari

On the iPhone and iPad, Safari is the standard browser. To not record a browser history, you can just stay in Private mode while surfing. When you do have a history to delete, go to Settings > Safari > Clear History & Website Data. Doing this not only takes out the history, but also cookies and other stuff. Plus, if the phone is signed into iCloud, it clears the history on iCloud as well as on other devices hooked into that iCloud account.
If you want to only delete data for select sites, go back to Settings > Safari and scroll down to Advanced > Website Data. After it loads (it can take a while) you'll see a listing of every website you've visited—and probably a lot you didn't, because it also records the sites serving third-party cookies. Click edit > minus symbol next to each to delete, or just swipe left for the same function.

Chrome

Google's Chrome browser is the standard with all Android phones, and is downloadable on iOS. In either, go to the three-dot () menu, select History, and you're looking at the list of all sites you've visited while cognito (as opposed to Incognito)—and that includes history across all Chrome browsers signed into the same Google account.
With iOS, you have the option to either click Edit or Clear Browsing Data at the bottom. If you click the latter (which is the only option on Android phones and tablets), you're sent to a dialog box (below) that allows the eradication of all browsing history, cookies, cached data, saved passwords, and autofill data—you pick which you want to delete. Android users get the added ability to limit deletion to an hour, a day, a week, a month, or the legendary "beginning of time."
Again, check My Activity later to see what may be stored online.
What's more, on iOS, there is a completely separate Google app for searching (iOSAndroid), with its own integrated browser. You can't delete the history of surfing within that Google app, though you can close all the tabs by clicking the Tabs icon at upper right, swiping one floating window right to delete, then clicking CLEAR ALL. That app's search history is stored at My Activity, of course.

Firefox

The Firefox browser is available for iOS or Android, free on both platforms. How you delete the browser history in each is a little different.
On iOS, tap the hamburger menu () at the bottom right and select Settings. Scroll down to the Privacy section, and select Data Management. On the next screen you can turn off collection of browser history (or data caching, cookies, and offline website data) entirely. Click the Clear Private Data link at the bottom to clear all of the above. Note in Settings there is also a toggle to Close Private Tabs, which shuts them all down when you leave the browser, should you be using such tabs o' stealth.
On Android, Firefox uses the three-dot menu () at upper right. Select History to see the list, and click CLEAR BROWSER HISTORY at bottom to nix them all from existence. If you click the menu and go to Settings > Privacy and check the box on Clear Private Data on Exit to get the option to clear the private data of your choice whenever you quit the browser.
Firefox Mobile

Opera

It's on iOS and Android, naturally. In fact, Opera for Android comes in two versions—a standard version and Opera Mini, which sends all websites and graphics through Opera servers to get compressed before you read them. Opera Mini is also on iPhone and even Windows Phone.
To clear history in Opera Mini on iPhone, clcik the O menu at bottom and select History, then click on the trash can icon to delete it. Or from the O menu, select Settings > Clear to find options to clear saved passwords, or browsing history, or cookies and data—or to hose all of them at once.
On Android, on the hamburger menu () select history and kill it with the trash can icon in the toolbar. Or go to hamburger menu to access Settings. You can scroll down to the Privacy section and find Clear Browsing Data...which lets you individually kill passwords, history, or cookies;
opera mobile