Two-dimensional electronic spectroscopy is a kind of nonlinear optical spectroscopy with both high time resolution and high frequency resolution. It can be used to observe the complex dynamics of a condensed molecular system. Meanwhile it is a very powerful tool to study the coherence between the electronic states or electronic and vibration states. In 2007, Flemming's group reported the long-lived quantum coherence observed in the energy transfer process in the light-harvesting antenna protein complex Fenna-Matthews-Olson at 77 K by means of two-dimensional electronic spectroscopy. Though it has been proved not to arise from the pure electronic coherence later, this discovery has greatly stimulated the exploration of the coherent energy transfer pathways possibly existing in the natural and artificial photosynthetic systems, and this is still a very active area nowadays. Here in this paper we briefly review the principle and set-up of the two-dimensional electronic spectroscopy, and also some of its applications in investigating coherent energy transfer in the photosynthetic and artificial systems, aiming to bring this novel spectroscopic tool into a wider application.