There's a lot of momentum to fix media management in Drupal 8 thanks to the Media Entity module. By using a combination of Media Entity, Entity Embed, Entity Browser and some media providers such as Media entity image you could add decent media handling in Drupal 8.

Then in Drupal 8.4, the Media Entity functionality was moved into a core module called Media. However, the core module was hidden by default. Now in Drupal 8.5 it's no longer hidden and you can install it yourself.

In this tutorial, you'll learn how to install and configure the Media module in Drupal 8 core. This tutorial is an updated version of the How to Manage Media Assets in Drupal 8 tutorial where we cover Media Entity.

Configuring Entity Embed and Entity Browser for the core Media module is essentially the same as with Media Entity. So if you have experience using Media Entity, then you'll be fine using the core Media module.