I have been using Remote desktop for quite some time now, but always had to use the mouse to navigate between my laptop and the remote computer. Today I came across a excellent resource from Windows Guides which listed the shortcut keys that can be used on a remote desktop.

Alt+Home > This works as a windows key replacement on the remote desktop, displaying the Windows Start menu.

Alt + Page Up > Works as a Alt+Tab replacement on the remote desktop, allowing you to switch between open application to the left.

Alt + Page Down > Works as a Alt+Tab replacement on the remote desktop, allowing you to switch between open application to the right.

Alt + Insert > Switches between programs in the most recently used order.

Alt + Del > Shows you the windows context menu on the remote desktop.

Ctrl + Alt + End > A Ctrl+Alt+Del replacement for the remote desktop.

You can view the entire list of shortcuts at Windows Guides: Keyboard Shortcuts to Use with Remote Desktop ^[1].