The martian moon Phobos is 26 km×22.8 km×18.2 km in size, and the major landforms on its surface are craters and grooves. We analyzed the visible craters on the surface of Phobos where ~1300 craters≥200 m in diameter, ~70 craters≥1 km, and ~30 craters≥2 km are identified; Stickney, the largest crater on Phobos, is about 8 km in diameter. Most craters are undoubtedly of impact origin although some small craters may be pits formed by drainage of regolith into subsurface fractures. The presence of the observed impact crater population implies that the upper hundreds of meters to a few kilometers of Phobos are heavily fractured. Using the available digital terrain model of Phobos (the dynamic version), the 24 craters larger than 2 km in diameter have been subdivided into three morphologic classes on the basis of their prominence; they are characterized by the following values of d/D ratios and maximum steepness of their inner slopes: >0.1 and >20°:9 craters; 0.05-0.1 and 10-20°:7 craters; and <0.05 and <10°:8 craters. This subpopulation of Phobos craters has a considerably larger number of craters with shallowly sloping walls compared to lunar highland craters; this may be due to several factors including the very small surface gravity of Phobos.Most craters on Phobos are bowl-shaped, some with a complex morphology in their interiors, including concentric, flat-bottomed and with central-mounds. The size of these craters with complex morphology is indicative of layering in the target material, both regolith covering bedrock and layers within the regolith. The thickness of the regolith estimated by different techniques varies from ~5 to 100 m. Layering within the regolith does not appear to be continuous, but more lens-like. The regolith of Phobos obviously accumulated by direct crater ejecta deposition and through the return of the ejecta high-velocity fraction that escaped to near-Mars space during the impact events. The Phobos regolith may be deficient in the <300 μm size fraction and contain martian material with concentrations ~250 ppm in the upper 0.5 m, and 1-2 orders of magnitude lower at greater depth. Downslope movement of material is revealed by downslope-trending albedo streaks and mounds on the floors and slopes of craters hundreds of meters to kilometers in size, commonly on crater inner slopes and sometimes on the outer slopes of crater rims. The albedo streaks are probably traces of geologically recent talus and avalanche emplacement. The mounds are interpreted to be landslide deposits. The different degrees of mound morphologic sharpness may be considered as an indication of their different age. Through the geologic analysis of the MRO HiRISE color images of Stickney crater and its vicinity, we documented the distribution and mutual relations of red and blue units of the surface material of Phobos. We conclude that the red and blue “primary” materials may form relatively large blocks comprising the interior of Phobos. Crater ejecta and downslope movement of material redeposit these materials, forming secondary and tertiary derivatives of these color material units and their mixtures. The grooves on Phobos are typically 100-200 m wide and several kilometers long and can be mapped in several intersecting systems (families) with approximately the same groove orientations within each family. They often crisscross relatively large craters, including crater rims, showing continuity with no gaps. Groove systems often intersect each other showing no lateral offsets at the intersections. At least one of groove families extends along a longitude for about 130o and this should have implications for groove formation mechanisms. Grooves similar to those on Phobos are seen on other small bodies: Eros, Lutetia and Vesta. Three different mechanisms of formation of Phobos grooves are discussed (1) grooves as fractures/faults, (2) grooves as tracks of rolling and bouncing boulders, and (3) grooves as chains of craters formed by ejecta from impact craters on Mars. The mechanism(s) of groove formation require additional studies. We conclude that the surface of Phobos is an arena for a variety of geologic processes. The leading role belongs to impact cratering with associated target destruction, material ejection from the crater and often from Phobos, and subsequent deposition partly with temporary residence in near-martian space. Shaking by impacts and surface stirring by day-night temperature changes cause granular surface material to move down along-slope driven by very low, but nevertheless efficient, surface gravity. A sample return mission is crucially important for a better understanding of the geological processes operating on Phobos. In addition to Phobos material, a returned sample will probably contain pieces of material from Mars. A series of outstanding questions to guide future exploration is listed.