As for the indoor units, they can either be the "ugly" ones (the indoor head units visible on the wall), recessed "cassettes", or they can use traditional A/C air handlers in a utility room to distribute conditioned air via existing duct-runs and registers.
There are also companies like Quilt that are making heat pump systems with much more attractive indoor wall units.
This isn't exactly new or unique to heat pumps (and some older heat pumps lack both), but as the technology has gotten cheaper and more reliable, coupled with the drive for better efficiency, it has become commonplace.