We will discuss an expansion for self-interacting random walks, developed in collaboration with Remco van der Hofstad. In some cases the expansion can be used to obtain a LLN and CLT. If the limiting velocity and/or variance are already known to exist, the expansion can still be useful in giving series representations for these quantities. We will use such a series representation to prove that in high dimensions, the speed of excited (cookie) random walk is a monotone increasing function of the excitation parameter, and discuss similar results that can be obtained for some other models.