In the first years after the emergence of deregulated power markets it became apparent that for the valuation of electricity derivatives we cannot simply rely on models developed for financial or other commodity markets. However, before adequate models can be put forward the unique characteristics of electricity (spot) prices have to be thoroughly analyzed. In particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of returns. In this paper we first analyze the stylized facts of electricity prices, then present two modeling approaches: jump-diffusion and regime-switching, which to some extent address the pertinent issues.