According to the first theoretical model of cometary tails by Alfven (1957) the region behind the gaseous non-magnetic planet looks like a long wake filled by draped magnetic field with the large BX component. The Martian magnetotail is a classical example of such a structure. Because of direct interaction of the solar wind with the planetary exosphere the wake region is filled by ions of the planetary origin. Observations of the planetary ion flow performed by mass analyzer IMA (ASPERA-3 experiment) onboard of Mars Express during last two years allow to reconstruct the main features of the Martian tail. Our statistical study shows that due to the finite Larmore radius of the heavy planetary ions (O+, O2+, etc), the ion spatial distribution is very asymmetric in the frame referred to the direction of convectional electric field of the solar wind. For instance, there is clear North-South asymmetry and some Dawn-Dusk asymmetry. Measurements show that the Martian magnetotail can be divided into two large regions. The first one is a magnetic pileup region, where the ions are accelerated mostly by pickup mechanism and where there is a pronounced velocity gradient from the magnetic pileup boundary to the center of the tail. The second region, "plasma sheet" is rather narrow layer elongated in North-South direction. Here an another ion acceleration mechanism acts, and the ions demonstrate an almost monoenergetic flow increased with the distance from the planet. The present talk discuss in details the magnetotail structure, different acceleration mechanisms, and different reasons of the observed asymmetry. The role of the magnetic anomalies in the plasma acceleration is discussed also.