to follow; to keep track of ....
Do you follow the murder case in the papers?
Why did they follow TV serials carefully?
We like to keep track of current events
to monitor
The situation should be very closely monitored
To monitor an apprentice's progress
To monitor a cardiac patient's pulse
to keep a close watch on ...
The police kept a close watch on the suspect
To keep watch on enemy troop movements along the
He had his wife watched by a private detective