Herein, different concepts for domain wall propagation based on currents and fields that could potentially be used in magnetic data storage devices based on domains and domain walls are reviewed. By direct imaging, we show that vortex and transverse walls can be displaced using currents due to the spin transfer torque effect. For the case of field-induced wall motion, particular attention is paid to the influence of localized fields and local heating on the depinning and propagation of domain walls. Using an Au nanowire adjacent to a permalloy structure with a domain wall, the depinning field of the wall, when current pulses are injected into the Au nanowire, was studied. The current pulse drastically modified the depinning field, which depended on the interplay between the externally applied field direction and polarity of the current, leading subsequently to an Oersted field and heating of the permalloy at the interface with the Au wire. Placing the domain wall at various distances from the Au wire and studying different wall propagation directions, the range of Joule heating and Oersted field was determined; both effects could be separated. Approaches beyond conventional field- and current-induced wall displacement are briefly discussed.