When a character gets better without medical treatment, emergency intervention, or other special sorts of intercession, the character generally heals by resting and avoiding more opportunities for Bad Things to Happen, for a certain period of time. Recovery Checks can automatically be made after a certain number of APs of time since the most recent damage taken to that particular Attribute, Power, or (most often) Current Condition, all depending on the kind of damage most recently done.
In our campaign, most kinds of damage, especially most damage done to Current Conditions, aren't made with the specific intent to kill. Resting Recovery Checks for this kind of injury are granted an hour (10 APs of time) after the most recent damage was done, and are pretty likely to succeed. Electro-stun guns, most gas grenades used in this campaign, and a majority of Superpowers will be the sort of thing the PC can try to shake off with an hour's rest and maybe some in-character symptomatic treatment. Players with the Fatiguing or Burn-out limitations on their powers (such as Taki's Exorcism power) will also need an hour to recover from most of their efforts, as will victims of attacks that specifically target superpowers.
On the other hand, certain attacks are lethal: these take an entire day (15 APs) of recovery time, before a Recovery Check can be made. A character who gets shot by a regular bullet-based firearm, or takes a ballista bolt to the chest, or has a building fall on him, or gets beaten down by a ring of angry RollerBoyz with baseball bats and shovels, is not going to just throw the effects off in a mere sixty minutes. The GM will specify whenever damage is this bad, and (before a Resting Recovery Check is even an option) urgent medical treatment becomes a really good idea if at all possible!
The time period for Resting Recovery checks is affected by the Regeneration Power: the APs of Regen are subtracted from the amount of time that would normally be needed, making both sorts of Recovery Checks come up more frequently. Regeneration itself is an Automatic Power, but since Recovery Checks are Dice Actions, Jennie is in the habit of saying that Feral Dice Action for a particular round (in a very long combat) is that she's going to "roll her Regen".