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

By default, creature spells are sorceries-speed spells, meaning you can only cast them during your own main phase when the stack is empty and you have priority (CR 307.1). However, there are several ways to cast creatures during another player's combat phase.

The most common exception is the keyword ability Flash (CR 702.8a), which allows a creature spell to be cast any time you could cast an instant — including during another player's combat phase, as long as you have priority. Similarly, effects like Teferi, Mage of Zhalfir's ability can grant all your creatures flash.

You also receive priority at several points during combat: after the beginning of combat step, after blockers are declared, after combat damage is dealt, and so on (CR 509.2, 510.2). At each of these points, if you hold priority or receive it, you may cast instant-speed spells — but NOT a vanilla creature spell without flash.

Example: Your opponent attacks with a 3/3. You have a Briarbridge Tracker (which has Flash) in hand. During the declare blockers step, you cast it at instant speed, and it enters as a 4/3, allowing you to use it as a blocker — because flash lets you cast it outside your main phase.

In summary: you can cast creature spells during another player's combat phase only if the creature has flash or a similar effect grants you that ability. Without flash, you must wait for your own main phase.