Can you cast a spell during another player's combat phase?

During another player's combat phase, you generally have the opportunity to cast instants and cards with flash. The combat phase contains several steps — Beginning of Combat, Declare Attackers, Declare Blockers, Combat Damage, and End of Combat — and players receive priority at the beginning of each step and after each time a player passes priority (CR 116.3, 117.3). Whenever you have priority, you may cast instants or use abilities.

The key restriction is spell type: you can only cast instants (or cards with flash, per CR 702.8a) during combat steps unless an effect specifically says otherwise. Sorceries, creatures, enchantments, and other non-instant, non-flash permanents cannot be cast during another player's turn at all (CR 307.1, 116.1).

There is one narrow exception: during the Declare Attackers step and Declare Blockers step, after the active player declares attackers or blockers, both players receive priority and may cast instants before moving on (CR 509.2, 510.1). This is a very common moment to cast combat tricks or removal spells.

Example: Your opponent attacks you with a 3/3 creature. You cast Giant Growth (an instant) on your 2/2 blocker during the Declare Blockers step, making it a 5/5. It now survives combat and destroys the attacker. This is perfectly legal because Giant Growth is an instant cast while you had priority.

In summary: instants and flash cards — yes, freely. Sorceries and other spell types — no, not during another player's combat phase.