Bose-Einstein condensation is a phase transition which atoms undergo when cooled near absolute zero temperature Since the theoretical prediction in 1924, and the spectacular experimental confirmation of Bose-Einstein condensation in 1995, a rich new field in physics has emerged studying ultracold degenerate quantum gases. Although these ultracold gases are very dilute, their properties are nevertheless strongly influenced by interatomic interactions. Usually, these interactions are dominated by short range, isotropic contact interactions. In contrast, the recently realised Bose-Einstein Condensate (BEC) of Chromium atoms contains long-range, anisotropic dipolar interactions leading to interesting new physics. In this graduation project, stationary states of such dipolar BECs in harmonic traps are investigated for various experimentally relevant parameters. Furthermore, the elementary excitations of the BEC are calculated, as well as its response to a rotating perturbation. Finally, some more advanced topics such as vortex interactions and condensate response to impurities are investigated.