We provided an analysis framework for analyzing and understanding electricity spot prices in deregulated European energy markets. We developed some econometric models to be suitable for use in such markets. First, we presented an overview of the electricity market. It enables us to identify the specific features of electricity spot prices and thus give us enough ground to propose the adequate model for modeling these prices. Next, we addressed the issue of modeling electricity spot prices in the oldest and the most promising power markets in the world, namely, the EEX and NordPool markets. To handle the dual the dual long memory phenomena encountered in both markets, price processes are modeled through an ARFIMA-FIGARCH model. Finally, we concentrated on the issues of building empirical models that consider the coexistence of long memory and non-linearity. We followed Zhang's hybrid methodology and introduced the new ARFIMA-LS-SVM model to describe both long memory and non-linearity simultaneously.