  The present review is devoted to our recent studies on the excitonic motion
in photosynthetic systems. In photosynthesis, the light photon is absorbed to
create an exciton in the antenna complex of the photosynthetic pigments. This
exciton then migrates along the chain-biomolecules, like FMO complex, to the
reaction centre where it initiates the chemical reactions leading to biomass
generation. Recently, it has been experimentally observed that the exciton
motion is highly quantum mechanical in nature i.e., it involve long time ($\sim
600$ femto sec) quantum coherence effects. Traditional semiclassical theories
like Forrester's and second Born master equations cannot be applied. We point
out why the 2nd Born non-Markovian master equation and its Markovian limit
(also called the Redfield master equation) cannot be used to explain the
observed long coherences. Briefly, the reason is that these approaches are
perturbative in nature and in real light harvesting systems various couplings
(system-system and system-bath) are of the similar order of magnitude. Various
new approaches are being developed to go beyond the above two limiting
theories. The present review is not a review in the usual sense of the word as
we summarize our own approaches and only refer to the literature for the other
ones. A brief introduction to the sophisticated 2D photon echo spectroscopy is
also given at the end with an emphasis on the underlying physics of the
multidimensional echo spectroscopies.
