What are the newest versions?

Check for updates to your Adobe Creative Cloud App

If your Creative Cloud app is not up to date, it will not find the newest versions of After Effects and Premiere Pro (or any other Creative Cloud software). You can choose Help > Check for Updates in the Creative Cloud Desktop app to see if there are any updates.
You’ll also find the newest version here: https://www.adobe.com/creativecloud/desktop-app.html

When the app is updated, open it and choose Applications > Updates to see if there are any updates available.

Read the System Compatibility Report

Well, just reading it will not help much, you’ll have to fix the problems it reports. When you start Premiere Pro or After Effects, you may get this dialog box. It will tell you what video driver updates and OS updates you need to install.

Click the Fix and Info buttons to get help fixing the problems. If you’re not allowed to update your system, Click the Export Report button and send the report to your IT department.

Check your OS

The System Compatibility Report will tell you to update your OS if it’s too old.

Check your GPU driver

Adobe Premiere Pro, After Effects and Premiere Rush all use the GPU a lot, and require updated drivers to work properly. Old drivers may cause instability, crashes and weird behavior. If you’re on macOS, updating your OS will update the GPU drivers, so if your macOS is up-to-date, you should be OK.

On Windows 10, you can update the GPU drivers manually. You may have to update drivers for both the Intel integrated GPU and your dedicated GPU from Nvidia or AMD. The links in the System Compatibility Report should take you to the place where you can download drivers. If not, try these links.

Drivers for Intel Graphics can be found here. I recommend that you choose the “Automatically update your drivers” option.
You’ll find drivers for Nvidia Graphics cards here. If you don’t know what model your card is you can right-click an empty space your desktop and select Nvidia Control Panel.
Drivers for AMD Radeon Graphics cards can be found here. I recommend that you use the “Auto-Detect and Install Radeon Graphics Drivers for Windows” option. If you’re not sure what model your cards is you can right-click an empty space your desktop and select AMD Radeon Settings.

Unfortunately, sometimes the newest drivers have bugs, so it may be smart to avoid the very latest drivers and stick to recommended/certified drivers like “Optimal drivers for Enterprise” or “Creator Ready drivers”.

Want a stable system for Premiere Pro and After Effects? Read Adobe’s recommendations

Optimizing your system for Premiere Pro and After Effects.
https://helpx.adobe.com/no/premiere-pro/kb/hardware-recommendations.html

To see what the newest released version is, go to What’s new in Premiere Pro

You can find your current version by clicking Help > About Adobe Premiere Pro or Adobe Premiere Pro > About Adobe Premiere Pro

To see what the newest released version is, go to What’s new in After Effects

You can find your version by clicking Help > About After Effects or Adobe After Effects > About After Effects

To see what the newest released version is, go to What’s new in Adobe Audition (this page has not been updated in a while, so you may want to check your Creative Cloud Desktop app too).