It has long been known that proteins are capable of transporting ions against a gradient in the chemical potential, using the energy available from a chemical reaction. This is called active transport. A well studied example is the Ca2+-transport by means of hydrolysis of adenosine triphoshpate (ATP) at the surface of the Ca2+-ATPase in sarcoplasmic reticulum. The cycle of events is known to be reversible, and has recently also been associated with a characteristic, and also reversible, heat production. We use the case of the Ca2+-ATPase to present and discuss various central theoretical approaches to describe active transport, with focus on two schools of development, namely the kinetic and the thermodynamic schools. Among the kinetic descriptions, Hill’s diagram method gives the most sophisticated description, reducing to the common Post-Albers scheme with simple enzyme kinetic reactions. Among the thermodynamic approaches, we review the now classical approach of Katchalsky and Curran, and its extension to proper pathways by Caplan and Essig, before the most recent development based on mesoscopic theory is outlined. The mesoscopic approach gives a non-linear theory compatible with Hill’s most general method when the active transport is isothermal. We show how the old question of scalar-vector coupling is resolved using rules for non-equilibrium thermodynamics for interfaces. Also thermal driving forces can then be accounted for. Essential physical concepts behind all methods are presented and advantages/deficiencies are pointed out. Emphasis is made on the connection to experiments.