How do I replay a match and step through it tick by tick?

Opening a match

Your tests: click Run test in Brain code's Test arena. Restart in the Arena runs the same test again from the start.
League matches: click a match's number under Rated series (League → Ladder), or Watch next to a finished match under Friendly matches (League → Live now & challenges). Tournament games have a ▶ button in the bracket on the tournament's page.

Under the field:

▶ / ⏸ plays and pauses. Space does the same.
⏮ and ⏭ step back or forward one tick. A match has 20 ticks a second.
Keys: ← and → step one tick; Shift+← and Shift+→ jump a second; Home goes to the start and End to the end.
The timeline can be dragged to any moment. Its marks show hits, bots destroyed and CPU faults.
The speed slider sets the speed as a percentage of real time. Double-click it for 100%.
Scanner arcs shows or hides where each bot's scanner is pointing.

The clock at the top left of the field shows the time and the tick, for example 12.35 s · tick 247 / 4800.

Events lists hits, bots destroyed and CPU faults, newest first. Click one to jump 1.5 s before it and play at half speed.
Teams shows every bot's hull at the moment you're watching.
Bot logs shows each bot's log up to that moment: what its program logged, and the damage it took.
Match gives the seed, the match's length and, after a test, each bot's average cycles per tick and faults.
Click a bot on the field to open a window with its machine and its parts. The match plays on meanwhile.

Stepping tick by tick while you read Bot logs is the best way to see exactly what your bot saw and decided at each moment.