Recent DMs are listed under the Direct Messages header in the left sidebar. If you want, you can customize your sidebar so you only see what's most important.
Click Direct Messages in the left sidebar to see all of your DMs.
Or, use a keyboard shortcut:
Mac: ⌘-Shift-K
Windows/Linux: Control-Shift-K
Tip: To remove a DM from your sidebar, click or tap the  icon.