Apple - Using The Terminal Command to Shutdown, Restart and Sleep My Mac?

The command you are after is shutdown. This informs all users that the machine is going to be shutdown and tells all apps to close files etc.

The command takes a parameter -h, -r or -s to shut down, restart or sleep the Mac.

The command has to be run as root so you need to use sudo.

e.g. to reboot the machine immediately

sudo shutdown -r now

e.g. to shutdown the machine in 60 minutes

sudo shutdown -h +60

From comments there are two things to be addressed

How shutdown works is by sending a sigterm to all processes which should then deal with that e.g. save open files etc. If they don't exit then they will get sent a SIGKILL which forces them to die with no chance to respond. The signals are not sent via the normal key message queue so Apps have to deal with this separately to the code that gets called from quit on the menu. A good app should call common code from both.

This other answer shows how to shutdown as if you hit the menu options. But note that apps can cancel this shutdown

Shut down without showing a confirmation dialog:

osascript -e 'tell app "System Events" to shut down'

Shut down after showing a confirmation dialog:

osascript -e 'tell app "loginwindow" to «event aevtrsdn»'

Restart without showing a confirmation dialog:

osascript -e 'tell app "System Events" to restart'

Restart after showing a confirmation dialog:

osascript -e 'tell app "loginwindow" to «event aevtrrst»'

Log out without showing a confirmation dialog:

osascript -e 'tell app "System Events" to  «event aevtrlgo»'

Log out after showing a confirmation dialog:

osascript -e 'tell app "System Events" to log out'

Go to sleep (pmset):

pmset sleepnow

Go to sleep (AppleScript):

osascript -e 'tell app "System Events" to sleep'

Put displays to sleep (10.9 and later):

pmset displaysleepnow

The four letter codes for the Apple events are listed in AERegistry.h.

All System Events commands above send Apple events to the loginwindow process. loginwindow is sent the same Apple events as above when you log out, restart, shut down, or put the the Mac to sleep normally. See Technical Q&A QA1134: Programmatically causing restart, shutdown and/or logout.

According to man shutdown, shutdown -h now and shutdown -r now send processes a TERM signal followed by a KILL signal.

According to the Daemons and Services Programming Guide, when you tell loginwindow to log out, processes that support sudden termination are sent a KILL signal, and processes that don't support sudden termination are terminated in different ways: Cocoa applications receive the applicationShouldTerminate: delegate method, foreground applications receive the kAEQuitApplication Apple event, background applications receive the kAEQuitApplication Apple event followed by a KILL signal, and daemons receive a TERM signal followed by a KILL signal after a few seconds.