Solid-solid phase transitions often exhibit hystereses, and a hysteresis indicates energy dissipation. Pseudoelasticity refers to a hysteretic loading-unloading characteristic observed in the stress-induced martensitic transformation of shape memory alloys. This paper describes the thermodynamic model of ideal pseudoelasticity, a largely schematized adaptation of the experimental observations, and it reviews the works of other authors on thermodynamics of pseudoelasticity. Different approaches vary widely, and we have chosen to put them into perspective by contrasting their assumptions and predictions against those of ideal pseudoelasticity.