SpaceX currently has two operational orbital launch vehicles, the Falcon 9 and Falcon Heavy. The company is also working on a third orbital launch vehicle called Starship.
Falcon 9
Falcon 9 is a partially reuseable medium lift launch vehicle that can carry cargo and crew into Earth orbit. The rocket has two stages. The first (booster) stage carries the second stage and payload to a certain altitude, after which the second stage lifts the payload to its ultimate destination. Both stages are powered by SpaceX Merlin engines, using cryogenic liquid oxygen and rocket-grade kerosene (RP-1) as propellants. The booster is capable of landing vertically to facilitate reuse, this feat was first achieved on flight 20 in December 2015.
Falcon 9 is human-rated for transporting NASA astronauts to the ISS. Falcon 9 is certified for the National Security Space Launch program and NASA Launch Services Program.
Falcon Heavy
Falcon Heavy is a partially reusable heavy-lift launch. The rocket consists of two strap-on boosters made from Falcon 9 first stages, a center core also made from a Falcon 9 first stage, and a second stage on top. Falcon Heavy has the highest payload capacity of any currently operational launch vehicle and the third-highest capacity of any rocket ever to reach orbit, trailing the Saturn V and Energia.
Falcon Heavy is certified for the National Security Space Launch program and NASA Launch Services Program.
Starship
Starship is a fully-reusable, super-heavy-lift launch vehicle. Starship is a two-stage-to-orbit launch vehicle, consisting of the Super Heavy booster stage and the Starship second stage or spacecraft. The spacecraft is planned to have four main variants: cargo, crew, propellant tanker, and lunar lander.
Both Starship rocket stages are designed for rapid reuse after a vertical landing, use liquid oxygen plus liquid methane for propellant, and are powered by Raptor engines. SpaceX intends that Starship will be able to deliver 100t (220,000 Ib) to low Earth orbit; once in orbit, the spacecraft can be refueled by Starship tankers to allow transit to higher orbits or other destinations. The spacecraft can then either enter the planet’s atmosphere and use its engines to land propulsively, or be left in outer space to serve as a lunar lander or a propellant depot.
As of July 2022, two Starship launch sites (Starbase in Texas and Kennedy Space Center in Florida) and two offshore platforms are under construction.
Starship is currently undergoing testing and is expected to have its first orbital spaceflight in November 2022.
Sources: Wikipedia and SpaceX