The planet Mars hosts an atmosphere that is perhaps the closest in terms of its meteorology and climate to that of the Earth. But Mars differs from Earth in its greater distance from the Sun, its smaller size, its lack of liquid oceans and its thinner atmosphere, composed mainly of CO(2). These factors give Mars a rather different climate to that of the Earth. In this article we review various aspects of the martian climate system from a physicist's viewpoint, focusing on the processes that control the martian environment and comparing these with corresponding processes on Earth. These include the radiative and thermodynamical processes that determine the surface temperature and vertical structure of the atmosphere, the fluid dynamics of its atmospheric motions, and the key cycles of mineral dust and volatile transport. In many ways, the climate of Mars is as complicated and diverse as that of the Earth, with complex nonlinear feedbacks that affect its response to variations in external forcing. Recent work has shown that the martian climate is anything but static, but is almost certainly in a continual state of transient response to slowly varying insolation associated with cyclic variations in its orbit and rotation. We conclude with a discussion of the physical processes underlying these long- term climate variations on Mars, and an overview of some of the most intriguing outstanding problems that should be a focus for future observational and theoretical studies.