Knowledge on light harvesting system and the reaction centres in plant during photosynthesis (C3, C4 Cam) are well established. Energy absorption& photon transport system in photosystem 1 (P680) and 2 (P700) for chemical reaction to produce ATP and NADPH which used in C fixation cycle is well documented. Hope you are interested in quantum physics in photosynthesis. Please refer this paper for more clarification.

Hsin, Johan Strümpfer, Melih Sener, Pu Qian, C. Neil Hunter, and Klaus Schulten. Energy transfer dynamics in an RC-LH1-PufX tubular photosynthetic membrane. New Journal of Physics, 12:085005, 2010

In quantum mechanics, all objects have wave-like properties (see de Broglie waves). For instance, in Young's double-slit experiment electrons can be used in the place of light waves. Each electron's wave-function goes through both slits, and hence has two separate split-beams that contribute to the intensity pattern on a screen. According to standard wave theory (Fresnel, Huygens) these two contributions give rise to an intensity pattern of bright bands due to constructive interference, interlaced with dark bands due to destructive interference, on a downstream screen. (Each split-beam, by itself, generates a diffraction pattern with less noticeable, more widely spaced dark and light bands.) This ability to interfere and diffract is related to coherence (classical or quantum) of the wave. The association of an electron with a wave is unique to quantum theory.

source: http://en.wikipedia.org/wiki/Coherence_%28physics%29#Quantum_coherence

Quantum coherence may refer to different things and need to be defined in the context that it is used. Some people used it to refer to coherent transport of excitations (ballistic transport), while other use it to discuss the excitation of a coherent superposition of eigenstates. Quantum coherence in biological systems is currently a hot topic with a heated debate especially following the claims that such effects are seen at physiological temperature in for example the Fenna-Matthews-Olson complex.

If you are interested in the topic, these three articles may be good for starting: http://chaos.in.ua/en/news/coherently-wired-light-harvesting-photosynthetic-marine-algae-ambient-temperature

And: http://www.nature.com/news/2011/110615/full/474272a.html

Also: http://iopscience.iop.org/1742-6596/302/1/012037/pdf/1742-6596_302_1_012037.pdf

I recommend reading the other side of the story as well. http://pubs.acs.org/doi/abs/10.1021/jp510074q

Article Exciton-vibrational coupling in molecular aggregates: Electr...

Article Vibronic phenomena and exciton-vibrational interference in t...

Article Energy transfer: Vibronic coherence unveiled

Article Two-dimensional spectroscopy of a molecular dimer unveils th...

Another interesting paper:

Article Perspective: Quantum or classical coherence?

I strong recommend the work of Collini et al. on NATURE| Vol 463|4 February 2010. Another important paper is Richard Hildner et al.

 Science 340, 1448 (2013);Quantum Coherent Energy Transfer over Varying Pathways in Single Light-Harvesting Complexes. 

Hope to find colleagues interested in quantum biology to have discussions and possible collaboration.

A new paper on the coherence in light-harvesting systems: https://www.nature.com/articles/s41557-018-0060-5

In my opinion, the application of the term "quantum coherence" to the processes of electron transfer and to energy transfer between LH complexes and RC does not reflect the essence and mechanism of the process itself. In bacterial photosynthesis, we have a vivid example of the manifestation of coherence of collective oscillations (oscillations of many particles) that initiate energy and electron transport. Despite the fact that this topic was discussed by me many years ago, I do not see any noticeable changes in the notion of the essence of the problem. And this situation will remain unchanged for many more years, because the desire to paraphrase and adapt other people's results in interpreting new own experimental data blinds the authors of a number of modern works. This is a scheme of attempts not to solve scientific problems, but to earn money. It is impossible to fight against it, but one thing is clear: the lack of ethics is incompatible with the effective promotion of an understanding of the essence of scientific problems...

Some examples of understanding the problem of coherence in bacterial photosynthesis can be found in my works. I will be glad if they will be of use to you and someone else.

Article Collective librations in the LH2 antenna systems and modulat...

Chapter Light harvesting and electron transfer in bacterial photosynthesis

Article Modulated broadening of the B800 absorption bands of the lig...

Article Temperature dependence of the broadening of the B850 absorpt...

Depends upon your background/interests the "unsolved" problem varies.

The most important thing is not whether are they unsolved, it is whether are you interested in them?

Please consult

https://www.researchgate.net/publication/332392867_Non-reciprocal_light-harvesting_nanoantennae_made_by_nature

It is about energy transfer between LH and RC.

we recently wrote a current opinion article about the evolution in our understanding of quantum effects in photosynthetic energy transfer.

https://reader.elsevier.com/reader/sd/93F90E060343B3FBCAF10D7F1BF11D73CC1DEAF72334EA2AB7EB6378924A752F23E42BABCE8CA39A0CCA838D089EF1E5

For a futuristic functional understanding of coherences, read this

https://www.nature.com/articles/nature21425

Please look out for this space, I may post another article about coherences in "electron transfer" in a month or so. That article may be more helpful in understanding what do we mean by coherences and when can they become functional.

Hope this one works

Article From coherent to vibronic light harvesting in photosynthesis

Thanks