  There is a remarkable characteristic of photosynthesis in nature, that is,
the energy transfer efficiency is close to 100%. Recently, due to the rapid
progress made in the experimental techniques, quantum coherent effects have
been experimentally demonstrated. Traditionally, the incoherent theories are
capable of calculating the energy transfer efficiency, e.g., (generalized)
F\"orster theory and modified Redfield theory. However, in order to describe
the quantum coherent effects in photosynthesis, the coherent theories have been
developed, such as hierarchical equation of motion, quantum path integral,
coherent modified Redfield theory, small-polaron quantum master equation, and
general Bloch-Redfield theory in addition to the Redfield theory. Here, we
summarize the main points of the above approaches, which might be beneficial to
the quantum simulation of quantum dynamics of exciton energy transfer in
natural photosynthesis, and shed light on the design of artificial
light-harvesting devices.
