Meaning of ‘Stay up’ Phrasal Verb in English

I like to stay up and read a good book before bedtime.

We're going to stay up and watch the midnight fireworks.

Don't stay up too late; we have an early meeting tomorrow.

The students decided to stay up studying for the final exams.

I need to finish this project, so I will stay up until it's done.

He had to stay up for a conference call with colleagues in different time zones.