The exploration of Mars has revealed the geological record of over 4 billion years of planetary history and, due to very low weathering rates and lack of plate tectonic recycling, the deposits associated with its climate history. Together with a significantly improved understanding of the nature and history of spin-axis/orbital (SA/O) changes, and improved atmospheric general circulation models (GCM), an outline of the nature of the climate history of Mars has become possible. We now know that the Amazonian period has been predominantly hyperarid and hypothermal with a global cryosphere and a horizontally stratified hydrological system, for the last ~3 Ga. SA/O changes, primarily obliquity, have resulted in the mobilization of polar ice and redistributed it to form mid-latitude ice sheets and even tropical mountain glaciers. In the Hesperian, outflow channels are interpreted to have emerged catastrophically from subsurface groundwater reservoirs and formed oceans in the northern lowlands, but recent work with GCMs suggest that these water-release events would produce extreme regional weather events and snowfall, but not oceans; new alternatives to the groundwater release hypotheses include top-down and bottom up heating and melting by emplacement of the abundant Hesperian-aged regional volcanic plains. A case can be made that a global cryosphere extended throughout the Hesperian. Abundant geological evidence exists for a “warm and wet” Noachian Mars (Mean Annual Temperature, MAT, >273K) (e.g., valley networks (VN), open/closed-basin lakes, abundance of phyllosilicate alteration minerals) that would imply a vertically integrated hydrologic system and a northern lowland ocean. Recent GCMs, however, predict a “cold and icy” climate with MAT ~225K, and an adiabatic cooling effect that results in deposition of snow and ice in the highlands (the Late Noachian Icy Highlands model). Perturbations to the ambient 225K “cold and icy” climate (e.g., volcanism, impact cratering, subsurface alteration reactions, etc.) are then required to raise atmospheric temperatures sufficiently to cause melting of surface snow and ice to produce the observed fluvial and lacustrine features. This outlined climate history forms the basis for a series of fundamental questions for future research and exploration.