Inversions include any posture that involves putting the heart above the head. Typically when people refer to inversions they are talking about headstand (sirsasana), handstand (ado mukha vrksasana), forearm balance (pincha mayurasana), shoulderstand (salamba sarvangasana) and plow pose (halasana), but given that the technical definition of an inversion is any posture that involves putting the heart above the head, most standing forward folds and also downward facing dog (ado mukha svanasana) fall into this category, as well.
Depending on the level of effort the pose requires, certain inversions can be energizing, but in theory all inversions are meant to be calming because they activate the parasympathetic nervous system. Again, depending on the level of effort involved, many inversions can be effective for strength building, especially when combined with transitioning to or from other postures, such as arm balances. Most postures in this category are safe for a variety of injuries, but again, given the risk of falling out of the posture, it’s best to move slowly and taking things on a case by case basis.