What is the state-of-the-art method for dealing with illumination issues in background subtraction?
The standard approach is to use a mixture of Gaussians to model the various laws that command the intensity of a pixel. In this approach, a pixel can be assigned several normal laws (with different mean and variance), each of them will model its value under different conditions.
Of course, only 1 Gaussian needs to be active at a time.

While the maximum number of Gaussians in the mixture is a (fixed) parameter, the parameters of each Gaussian are learned online.
You can find an example implementation in the OpenCV library.

A few years ago, someone (sorry, i can't find the name anymore) proposed an interesting alternative approach: using variations of the image gradient orientation instead of variations of the light intensities.
The gradient orientation has the advantage of being contrast invariant, making it more robust to illumination changes.
Intuitively, it works because the gradient orientation is tied to the shapes in the image, not to their color or luminosity.