The mini split.
Refrigerant to the room instead of air through ducts. Useful for the room central air cannot reach.
A mini split moves refrigerant to the room instead of moving air through ductwork.
An outdoor unit connects by a small line set to one or more indoor heads, usually mounted high on a wall. Each head has its own coil and fan, and typically its own control, so each space is conditioned independently.
A multi-zone system runs several heads off one outdoor unit.
Where it makes sense in a Valley house
A room central air cannot reach. A converted garage, an addition, a casita, an office over a garage. Running duct to those is often more disruptive and more expensive than a ductless head.
A second floor the main system loses, which is a very common Phoenix situation and covered in the upstairs guide.
A room with wildly different load, like a west-facing room with a lot of glass, which would otherwise force the whole house to run colder.
A house with no ducts at all, which is rare here but exists.
The advantages
No duct losses, which in a 150 degree Phoenix attic is a genuinely large number. Independent control per room. Nearly all of them are inverter driven, so they run long and slow rather than cycling, which suits this climate.
The trade-offs
It is visible. A head on the wall is a design decision some people dislike.
Condensate. Each head produces water, and most use a small condensate pump rather than gravity. That is another thing that can fail, over drywall.
Filters. Each head has its own, and they get neglected because they are not where people look for a filter.
Service. Parts are often brand-specific rather than universal, which affects both availability and price.
What this site covers
Installation of a mini split is not work that can be done here: it is a refrigerant circuit install and frequently a permit question, so it goes to a licensed Arizona contractor. Diagnosis and small work on an existing one is a different matter, and worth a call rather than an assumption.