I'm running late. Can I still bowl once the game has started?

Yes, by default (a league may adopt its own tardy rule, such as a cut-off frame):

• You start bowling, with your score counting, from the frame your team is currently bowling.
• For each frame you missed, you get one-tenth of your absentee score (absentee score = your average minus 10, unless the league sets another number).
• The partial game doesn't count toward your average unless the league keeps averages frame by frame.

Example: average 160, absentee score 150. You arrive in time for the 4th frame, missing 3 frames: you're credited 3 × 15 = 45 pins for those frames plus whatever you bowl in frames 4 to 10.

Your team still needs a legal lineup present by the end of the first frame (or the frame set by league rule), even if a late bowler is on the way.