Results by Neukum et al. (2001) and Ivanov (2001) are combined with crater counts to estimate ages of Martian surfaces. These results are combined with studies of Martian meteorites (Nyquist et al., 2001) to establish a rough chronology of Martian history. High crater densities in some areas, together with the existence of a 4.5 Gyr rock from Mars (ALH84001), which was weathered at about 4.0 Gyr, affirm that some of the oldest surfaces involve primordial crustal materials, degraded by various processes including megaregolith formation and cementing of debris. Small craters have been lost by these processes, as shown by comparison with Phobos and with the production function, and by crater morphology distributions. Crater loss rates and survival lifetimes are estimated as a measure of average depositional/erosional rate of activity. We use our results to date the Martian epochs defined by Tanaka (1986). The high crater densities of the Noachian confine the entire Noachian Period to before about 3.5 Gyr. The Hesperian/Amazonian boundary is estimated to be about 2.9 to 3.3 Gyr ago, but with less probability could range from 2.0 to 3.4 Gyr. Mid-age dates are less well constrained due to uncertainties in the Martian cratering rate. Comparison of our ages with resurfacing data of Tanaka et al. (1987) gives a strong indication that volcanic, fluvial, and periglacial resurfacing rates were all much higher in approximately the first third of Martian history. We estimate that the Late Amazonian Epoch began a few hundred Myr ago (formal solutions 300 to 600 Myr ago). Our work supports Mariner 9 era suggestions of very young lavas on Mars, and is consistent with meteorite evidence for Martian igneous rocks 1.3 and 0.2 - 0.3 Gyr old. The youngest detected Martian lava flows give formal crater retention ages of the order 10 Myr or less. We note also that certain Martian meteorites indicate fluvial activity younger than the rock themselves, 700 Myr in one case, and this is supported by evidence of youthful water seeps. The evidence of youthful volcanic and aqueous activity, from both crater-count and meteorite evidence, places important constraints on Martian geological evolution and suggests a more active, complex Mars than has been visualized by some researchers.