As the name suggests, these telescopes use both lenses and mirrors. There are many variations to these. They include the Maks and the SCTs. The Cassegrain telescopes are catadioptric. My guide on using telescopes to view planets gives the pros and cons of some popular examples of these.
Because of their compact design, the catadioptric telescopes are more portable. Like reflectors, they need collimation, but far less frequently. They can stay aligned and may only need collimation every few years.
These are versatile, being great for deep sky use as well as for viewing planets and the moon.