The two moons of Mars are Phobos and Deimos. They are irregular in shape. Both were discovered by American astronomer Asaph Hall in August 1877 and are named after the Greek mythological twin characters Phobos and Deimos who accompanied their father Ares into battle. Ares, the god of war, was known to the Romans as Mars.
Enhanced color image of Phobos (MRO, 23 March 2008)
Enhanced color image of Deimos (MRO, 21 February 2009)
Asaph Hall III, discoverer of Phobos and Deimos
Apparent sizes of the moons of Mars, Deimos and Phobos, and the Moon as viewed from the surface of their respective planets (Mars' moons imaged by the Curiosity rover, 1 August 2013)
Phobos is the innermost and larger of the two natural satellites of Mars, the other being Deimos. The two moons were discovered in 1877 by American astronomer Asaph Hall. It is named after Phobos, the Greek god of fear and panic, who is the son of Ares (Mars) and twin brother of Deimos.
Enhanced color image of Phobos, as captured by the Mars Reconnaissance Orbiter. Stickney, the largest crater on Phobos, is on the right.
Asaph Hall III, discoverer of Phobos
The Phobos monolith (right of center) as taken by the Mars Global Surveyor (MOC Image 55103, 1998).
Image: Stickney mro