These days the most exciting research I think is in path guiding and many-light sampling techniques.
[0] https://research.nvidia.com/sites/default/files/pubs/2013-07...
[1] https://research.nvidia.com/publication/understanding-effici...
[2] https://research.nvidia.com/publication/2021-06_Alias-Free-G...
Its primary purpose is to be be used by artists for SFX type work, but if you're looking to make really accurate renderings of complex lighting scenes, for e.g. accurate architectural renderings, I would not use cycles and look at luxcore [0][1] instead.
Basically what you're doing in MC is estimating expected values (and thereby integrals: average height times base width equals area under the graph) using random numbers, to be roughly thought of as a rnd() function which gives you back a float in [0,1).
However, using actual proper random number generators has a very slow convergence rate, as the random numbers chosen will tend to clump; on the other hand, if you just use a perfectly uniform distribution, you'll suffer from correlation problems.
Consider a 1-D numerical integration problem, and instead of using rnd() to pick points in your integrand range, you start with some seed value in [0,1), and each time you need a new random number, you add phi-1 to the existing number and mod with 1.0 to get the new number. If you plot this sequence on a [0,1) number line, you'll see that it divides up the interval into finer pieces really nicely, magically keeping a good distance from all the previous values, without even knowing them!
Why does this work? Well, there's a lot of beautiful theory about phi (also relating to biology and nature, e.g. seashells and the distribution of sunflower seeds), in particular how it is in some sense (continued fraction) the "most irrational" number. Does it work well for other numbers, and can it be extended to higher dimensions? Sure, there are some interesting things you can do: http://extremelearning.com.au/unreasonable-effectiveness-of-...
This isn't even scratching the surface of things like the Halton, Hammersley and Sobol sequences, the human visual response to different kinds of noise that makes blue noise preferable, etc. Here's a wealth of recent research on all that: https://sites.google.com/view/myfavoritesamples
Rendering is particularly beautiful in that it touches on so many fields, from pure maths, to applied maths and numerical methods, to physics, to human biology and perception, aesthetics, both low- and high-level programming concerns, even philosophy: if we can simulate visual reality to such high precision, it lends credence to the idea that we ourselves are simulated. To me the apparently obvious truth of this is up there with understanding that the iron that makes our blood red can only be formed in supernovae.
(h/t Leonid Petrov, Victor Kleptsyn)
[1] https://www.wired.com/2012/12/what-does-randomness-look-like...
[2] https://www.actuaries.org.uk/system/files/documents/pdf/0481...
IIRC, he moved on from inventing a brand new rendering methodology inspired from oldie research in nuclear physics [0] to designing the S2 system at Google [1] to building one of the largest money-making machines in the ads world at Google [2][3].
Not exactly your average engineer.
[0] https://en.wikipedia.org/wiki/Nicholas_Metropolis
[1] https://en.wikipedia.org/wiki/Eric_Veach
[2] https://uwaterloo.ca/math/people-profiles/eric-veach
[3] https://www.businessinsider.com/unsung-google-heros-2011-5?r...
For others who like opensource renderers: Appleseed (which Franz is lead developer of) is amazing, check it out! https://appleseedhq.net/
I've spent my entire life studying this stuff and feel extremely lucky on so many levels: that we have these incredible computers which can actually do the computation, that we happen to have such a powerful theory that can model and even predict visual reality, and perhaps most of all, that a single person can learn all this stuff and carry it around with them everyday - it's really changed how I see the world.
My deepest thanks go to those who have developed and passed all this on through their papers and books; it's literally what I'm getting the meaning of life from.