Barocaloric materials have the potential to offer greener and more efficient alternatives to conventional refrigerants that exploit vapor compression for cooling and heating applications. The barocaloric effect, a temperature change in response to hydrostatic pressure, is widespread in materials; however, only in the last few years have giant and colossal barocaloric effects approaching those of commercial hydrocarbon refrigerants been discovered. These barocaloric effects are associated with large changes in the degrees of freedom within the material and can take various forms. Here, we discuss this variety and categorize barocaloric materials based on the degree of freedom that underpins the barocaloric effects. We use this framework to identify material families to explore for potential barocalorics.