For responsive web design, generally speaking anything that works in an older browser will continue to work in all newer browsers that have been released after it. This means that when you think about the technology and features you use to build your website, what you will be able to use is limited by the oldest browser you need to support.
For example, IE8 doesn't support CSS Media Queries, so any kind of 'responsive' design that must support IE8 will need some JavaScript to work. If you are developing a site that's IE9+ you can use CSS Media Queries.
Flexbox and Grid also have different support, you can check on caniuse.com to see the support in browsers:
It is possible to build sites using features more advanced than the oldest browser you need and to try to handle those older browsers separately, but that gets complicated quickly. An older layout will work just fine in a newer browser without extra help, so it's a lot better to build with the oldest browser you actually must support in mind and then you can be sure it will work everywhere.