Despite his difficulties with his board of directors and investors, Elon Musk is full-speed ahead for a manned Mars mission by 2024. Of course, that depends on a few other tests going off without a hitch, or even a "rapid unscheduled disassembly," as Musk likes to call rocket failures.
The idea is to start test launches from a facility in southern Texas by the end of this year, and then to launch two jumbo versions of their flagship orbital rocket (named the "Big Falcon Rocket" or BFR) to Mars by 2022. These first missions will carry payloads of supplies (such as food, machinery and oxygen harvesters) to the red planet for use by crews who will arrive later. The plan is refuel the rockets while in Earth orbit so that they can reach Mars without having to lift the weight of the extra fuel at initial launch. The 2022 target date is because this is the next time Earth and Mars will be at their closest distance.
In 2023, a manned mission around the moon will be attempted in order to test the crew ship. Japanese billionaire Yusaku Maezawa has paid an undisclosed sum to be the first passenger on this outer space test. For his financial support, he will also be bringing along six to eight other astronauts of his choosing.
If all goes well, the first manned mission should be ready to go by 2024, with a landing on Mars by 2025. At that time, the first crew will begin construction on "Mars Base Aplha" with eventual cities on the planet by sometime in the 2030s.
More at the SpaceX website and here.