in absence of more details, i'd split problems of illumination in virtual world into 3 groups
material responds to sum of direct and indirect light
1. material response to light
usually implemented in shader
problems are e.g. how to most efficiently support many lights and feed all information required by shader.. lot's of implementation work, especially in area of simulation of geometry details and their response to lighting, but nearly no open problems.
2. amount of direct light = visibility, shadows
usually implemented as a) lightmaps b) shadowmaps c) stencil shadows d) projected shadows
again, lots of implementation work, nothing interesting
the only research i know about happens in field of large scale world realtime shadows -> various derivations of shadow mapping with better and better quality.
limited progress happens in physically correct soft shadows, several techniques exist but noone uses them because correct is 2x slower than simply blurred.
3. amount of indirect light (reflected in multiple bounces)
usually precomputed for fixed scene and ignored for dynamic, because it's difficult.
for precomputations, no problem if you have enough time, many good old techniques exist. however it's still open problem how to do it most efficiently and reliably. v.havran works on paper that could significantly boost state of the art here.
for realtime rendering with dynamic scene/lights, it's very open problem.
first solutions start to appear, e.g.
demo and article i wrote 1 year ago. accidentally i plan to release new demo with realtime global illumination soon (check
lightsprint in a few weeks)
of course it's very incomplete description, throw in few more words about your problem
