The role of non-trivial quantum mechanical effects in biology has been the subject of intense scrutiny over the past decade. Much of the focus on potential "quantum biology" has been on energy transfer processes in photosynthetic light harvesting systems. Ultrafast laser spectroscopy of several light harvesting proteins has uncovered coherent oscillations dubbed "quantum beats" that persist for hundreds of femtoseconds and are putative signatures for quantum transport phenomena. This review describes the language and basic quantum mechanical phenomena that underpin quantum transport in open systems such as light harvesting and photosynthetic proteins, including the photosystem reaction centre. Coherent effects are discussed in detail, separating various meanings of the term, from delocalized excitations, or excitons, to entangled states and coherent transport. In particular, we focus on the time, energy and length scales of energy transport processes, as these are critical in understanding whether or not coherent processes are important. The role played by the protein in maintaining chromophore systems is analysed. Finally, the spectroscopic techniques that are used to probe energy transfer dynamics and that have uncovered the quantum beats are described with reference to coherent phenomena in light harvesting.
Keywords: Light harvesting; Photosynthesis; Protein; Quantum biology; Quantum coherence.