This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years.The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine,the stochastic heat engine constructed from a Brownian particle,and Feynman’s ratchet as a heat engine are presented.It is found that:the efficiency at maximum power exhibits universal behavior at small relative temperature differences;the lower and the upper bounds might exist under quite general conditions;and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time. This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman’s ratchet as a heat engine are presented. It is found that: the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.