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Solar variability influences the climate of a planet by radiatively forcing changes over a certain timescale; orbital variations of a planet, which yield similar solar forcing modulations, can be studied within the same scientific context. It is known for Earth that obliquity changes have played a critical role in pacing glacial and interglacial eras. For Mars, such orbital changes have been far greater and have generated extreme variations in insolation. Signatures associated with the presence of water ice reservoirs at various positions across the surface of Mars during periods of different orbital configurations have been identified. For this reason, it has been proposed that Mars is currently evolving between ice ages. The advent of climate tools has given a theoretical frame to the study of orbitally-induced climate changes on Mars. These models have provided an explanation to many puzzling observations, which when put together have permitted reconstruction of almost the entire history of Mars in the last 10 million years. This paper proposes to give an overview of the scientific work dedicated to this topic. [ABSTRACT FROM AUTHOR]