In this thesis we address the subject of strong electron-phonon coupling in pyramidal quantum dots and pursue detailed physical, analytical and numerical investigations. The strong coupling polaron states in a pyramidal GaAs/AlGaAs quantum dot are computed numerically with an enhanced matrix diagonalization method that accounts for the particular structure of the Hamiltonian and uses an irregular reciprocal space discretization. Electron-electron interactions and multiple phonon interactions are neglected. We study quantum dots with either three or four confined electron states associated with two or three electron levels, respectively. Further, we develop a set of analytical tools to predict and interpret the polaron states of a more general model of quantum dots. Applying these tools to the particular case allows a complete classification of the polaron states and reveals new physical insight.