1.
Suddenly snatch or lift up, as in The wind caught up the kite and sent it high above the trees. [First half of 1300s]
2.
Also,
catch up with. Come from behind, overtake. This usage can be either literal, as in You run so fast it's hard to catch up with you, or figurative, as in The auditors finally caught up with the embezzler. [Mid-1800s]
3.
Become involved with, enthralled by, as in We all were caught up in the magical mood of that evening. [Mid-1600s]
4.
Also,
catch up on or with. Bring or get up to date, as in Let's get together soon and catch up on all the news, or Tonight I have to catch up with my correspondence. [First half of 1900s]