Random projection is a simple technique that can often provide insight into questions such as "why is it good to have a large margin?" or "what are kernels really doing and how are they similar to feature selection?" In this talk I will describe some simple learning algorithms using random projection. I will then discuss how, given a kernel as a black-box function, we can use various forms of random projection to extract an explicit small feature space that captures much of the power of the given kernel function.