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Cobalt-based full-Heusler compounds with composition Co2M′ Z (where M ′ is a transition metal and Z is a main group element) are attracting attention due to their predicted half-metallic behaviour, a considerably desired property for spin-dependent electron transport devices. Knowledge of the basic magnetic properties of these materials, in particular in the form of thin films, is required both to fully exploit these promising materials, and to understand their underlying electronic structure and establish structure-property relationships. In this Topical Review, we present a survey of the magnetic anisotropy, exchange, and damping of Co2M ′ Z compounds. These properties are directly related to spin-spin and spin-orbit interactions.