  We discuss the possibility of reaching the Carnot efficiency by heat engines
(HEs) out of quasi-static conditions at nonzero power output. We focus on
several models widely used to describe the performance of actual HEs. These
models comprise quantum thermoelectric devices, linear irreversible HEs,
minimally nonlinear irreversible HEs, HEs working in the regime of low
dissipation, over-damped stochastic HEs and an under-damped stochastic HE.
Although some of these HEs can reach the Carnot efficiency at nonzero and even
diverging power, the magnitude of this power is always negligible compared to
the maximum power attainable in these systems. We provide conditions for
attaining the Carnot efficiency in the individual models and explain practical
aspects connected with reaching the Carnot efficiency at large power output.
Furthermore, we show how our findings can be tested in practice using a
standard Brownian HE realizable with available micromanipulation techniques.
