Various browser software titles use different code processing engines that get updates and enhancements at different rates. This poses a challenge to developers regarding implementation of certain HTML features. Web developers have been dealing with these types of hurdles and speed-bumps ever since the early days of the internet. Dealing with browser differences is part of your job as a web developer.
As you author documents it is a good idea to test them using all of the different popular browser environments, just to make sure each aspect works as intended across the board. If you find that one of the browsers does not support a feature that all of the others do, you may have to come up with a workaround for that specific troublesome browser.
Your documents should also be user friendly for people on mobile devices and tablets. Be sure to test your websites and web applications on all of the most popular mobile devices and tablets to make sure they are finger friendly. Using CSS3 Media Queries allows authors to make responsive layouts changes relative to screen sizes.
Google has a great online Mobile-Friendly Test software you can use to quickly check your site pages for smart phone screen compatibility. Tablets are not really a consideration because in landscape mode they display a layout well over 1000px in width no problem, the real challenge is setting up a layout compatible with tiny smart phone screens.