Spin caloritronics refers to research efforts in spintronics when a heat current plays a role. In this review, we start out by reviewing the predictions that can be drawn from the thermodynamics of irreversible processes. This serves as a conceptual framework in which to analyze the interplay of charge, spin and heat transport. This formalism predicts tensorial relations between vectorial quantities such as currents and gradients of chemical potentials or of temperature. Transverse effects such as the Nernst or Hall effects are predicted on the basis that these tensors can include an anti-symmetric contribution, which can be written with a vectorial cross-product. The local symmetry of the system may determine the direction of the vector defining such transverse effects, such as the surface of an isotropic medium. By including magnetization as state field in the thermodynamic description, spin currents appear naturally from the continuity equation for the magnetization, and dissipative spin torques are derived, which are charge-driven or heat-driven. Thermodynamics does not give the strength of these effects, but may provide relationships between them. Based on this framework, the review proceeds by showing how these effects have been observed in various systems. Spintronics has become a vast field of research, and the experiments highlighted in this review pertain only to heat effects on transport and magnetization dynamics, such as magneto-thermoelectric power, or the spin-dependence of the Seebeck effect, the spin-dependence of the Peltier effect, the spin Seebeck effect, the magnetic Seebeck effect, or the Nernst effect. The review concludes by pointing out predicted effects that are yet to be verified experimentally, and in what novel materials the standard thermal spin effects could be investigated.