Climbing is an interesting form of quadrupedal locomotion on vertical substrates, and also a popular recreational activity. However, a theory of locomotor energetics of climbing has not been devised yet. Here we discuss an analytical model, based on simple physical principles, that gives the energy cost as a function of the vertical speed. We found that the energy cost monotonically decreases with speed, so that to minimize the energy spent to climb one should ascend at the highest possible speed. We propose that the actual climbing speed derives from the requirement of minimizing simultaneously the work per unit time as well as the work per unit length. Our predictions are in excellent agreement with measurements carried out on elite climbers.