to observe the behaviour or communications of individuals or groups (see surveillance)

Clinical monitoring for new medical drugs

Condition monitoring

Structural monitoring

Website monitoring

Network monitoring

Election monitoring

Biomonitoring is the science of inferring the ecological condition of an area by examining the organisms that live there. Although biomonitoring can occur in any ecosystem, it is most often used to assess water quality of rivers, lakes, streams, and...

Monitoring competence at a task.

to observe a situation for any changes which may occur over time, using a monitor or measuring device of some sort:

Baby monitor, medical monitor, Heart rate monitor

Futures monitoring, Media monitoring service