A major goal of Computer Graphics algorithms is to create images of virtual scenes that are as close as possible to what the scenes would look like in reality. This is called photorealistic rendering, and is commonly used in virtual prototyping, e.g., in the automotive industry or in architecture. Such photorealistic rendering implies accurate computation of the effects of light transport and reflection in the scene, which is a very computationally expensive process. The process is expensive partly because illumination behaves in a highly complex manner: in some places, it varies very rapidly, while in others it changes smoothly. However, through a complete and thorough analysis of the equations of light transport, we believe that we can extract information about this behaviour, and use it for more efficient computations. We will analyze light transport using three different approaches: frequency analysis, dimensionality analysis and 1st-order analysis. Each will be used for two different applications of lighting simulation: either offline, high-quality simulation or interactive simulations. The key novelty of our approach stems from the extraction of compact and efficient quantities from the above analysis, which are used to design innovative algorithms, with significant gains in both time and storage. In what follows, we will present examples of both the analysis and its application, e.g., the use of the covariance matrix to encode frequency properties of light transport and its potential to dramatically improve the speed of Monte-Carlo path-tracing.