Multiline editing in Visual Studio Code
Solved using just two steps!
Ctrl + F
Alt + Enter
It's equal to Sublime Text's Alt + F3.
Box Selecting
Windows: shift + alt + Mouse Left Button
macOS: shift + option + Click
This is contrary to what is mentioned in an answer to Does Visual Studio Code have box select/multi-line edit?.
You can just Alt + click for additional cursors. And as already mentioned, Ctrl + Alt + ↑ or ↓.
On Windows, you hold Ctrl+Alt while pressing the up ↑ or down ↓ arrow keys to add cursors.
Mac: ⌥ Opt+⌘ Cmd+↑/↓
Linux: Shift+Alt+↑/↓
Note that third-party software may interfere with these shortcuts, preventing them from working as intended (particularly Intel's HD Graphics software on Windows; see comments for more details).
If you experience this issue, you can either disable the Intel/other software hotkeys, or modify the VS Code shortcuts (described below).
Press Esc to reset to a single cursor.
Or, as Isidor Nikolic points out, you can hold Alt and left click to place cursors arbitrarily.
You can view and edit keyboard shortcuts via:
File → Preferences → Keyboard Shortcuts
Documentation:
https://code.visualstudio.com/docs/customization/keybindings
Official VS Code Keyboard shortcut cheat sheets:
https://code.visualstudio.com/shortcuts/keyboard-shortcuts-windows.pdf
https://code.visualstudio.com/shortcuts/keyboard-shortcuts-macos.pdf
https://code.visualstudio.com/shortcuts/keyboard-shortcuts-linux.pdf