With the scarcity of factual data and the difficulty of applying crucial tests, many of the properties of the Martian surface remain a mystery; the planet may become a source of great surprises in the future. In the following, the conclusions are enumerated more or less in the order of their reliability, the more certain ones first, conjectures or ambiguous interpretations coming last. Even if they prove to be wrong, they may serve as a stimulus for further investigation. Impact craters on Mars, from collisions with nearby asteroids and other stray bodies, were predicted 16 years ago (5-7) and are now verified by the Mariner IV pictures. The kink in the frequency curve of Martian crater diameters indicates that those larger than 20 kilometers could have survived aeolian erosion since the "beginning." They indicate an erosion rate 30 times slower than that in terrestrial deserts and 70 times faster than micrometeorite erosion on the moon. The observed number, per unit area, of Martian craters larger than 20 kilometers exceeds 4 times that calculated from the statistical theory of interplanetary collisions with the present population of stray bodies and for a time interval of 4500 million years, even when allowance is made for the depletion of the Martian group of asteroids, which were more numerous in the past. This, and the low eroded rims of the Martian craters suggest that many of the craters have survived almost since the formation of the crust. Therefore, Mars could not have possessed a dense atmosphere for any length of time. If there was abundant water for the first 100 million years or so, before it escaped it could have occurred only in the solid state as ice and snow, with but traces of vapor in the atmosphere, on account of the low temperature caused by the high reflectivity of clouds and snow. For Martian life there is thus the dilemma: with water, it is too cold; without, too dry. The crater density on Mars, though twice that in lunar maria, is much smaller than the "saturation density" of lunar highlands. Many primeval craters, those from the last impacts which formed the planet, must have become erased, either by late impacts of preferentially surviving large asteroids or by a primeval atmosphere which rapidly escaped. The tenuous Martian atmosphere may have originated entirely from outgassing of surface rocks by asteroidal impacts, which also could have produced some molten lava. The role of genuine volcanism on Mars must have been insignificant, if any. The large amplitude in temperature indicates that the Martian upper soil, equally in the bright and the dark areas, is of a porous unconsolidated structure, with a thermal conductivity as low as that of atmospheric air. Limb darkening at full phase in green, yellow, and red light indicates absorption by atmospheric haze, aerosols, and dust. The loss of contrast in the blue and violet is caused by stronger absorptivity of the haze, which is almost as dark as soot, and not by a true decrease in contrast of the surface markings. Photometric measurementsin the blue reveal a residual contrast of 5 to 7 percent between the markings in 1958, invisible to the eye at a time when there was no "blue clearing." The surface brightness of the maria was surprisingly uniform in 1958 (late summer in the southern hemisphere), while the continentes showed considerable variation. In view of the spotty microstructure of the Martian surface as revealed by Mariner IV, and the lack of a sharp border between a mare and a continens, it seems that all the difference consists in the relative number of small dark and bright areas in the surface mosaic. If there is vegetation on Mars, it should be concentrated in the darkarea elements, measuring 10 to 100 kilometers. Vegetation is the best hypothesis to account for seasonal changes in the maria and for the persistence of these formations despite dust storms of global extent. Survival of vegetation in the extreme dryness of the Martian climate could depend on the low night-time temperature and deposition of hoarfrost, which could melt into droplets after sunrise, before evaporating. If not vegetation, it must be something thing specifically Martian; no other hypothesis hitherto proposed is able to account for the facts. However, the infrared bands which at one time were thought to be associated with the presence of organic matter, belong to heavy water in the terrestrial atmosphere. The conversion of a former bright area into a dark one in 1954, over some 1 million square kilometers, is the largest recorded change of this kind. Even on the vegetation hypothesis, it eludes satisfactory explanation. Relatively bright areas observed in the blue and violet in polar regions and elsewhere on the limb can be explained by a greater transparency of the atmosphere,its dust content being decreased by a downward (anticyclonic) current. The surface, of a greater reflecting power than the atmospheric smoke, then becomes visible. The sudden explosion-like occurrence of yellow or gray clouds, reducing atmospheric transparency and surface contrast, could be due to impacts of asteroids; in such a case, however, the number of unobservable small asteroids, down to 30 to 40 meters in diameter, should greatly exceed the number extrapolated from the larger members of the group. A "meteoritic" increment in numbers, instead of the asteroidal one, would be required. special observations with large Schmidt telescopes could settle this crucial question. The Martian "oases," centers of "canal" systems, could be impact creters. The canals may be real formations, without sharp borders and 100 to 200 kilometers wide, due to a systematic alignment. of the dark surface elements. They may indicate cracks in the planet's crust, radiating from the point of impact.