Google's Chrome browser is the standard with all Android phones, and is downloadable on iOS. In either, go to the three-dot (horizontal ellipsis) 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 (iOS, Android), 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.