Magnetic domain wall (DW) dynamics is currently attracting tremendous interest both from a fundamental point of view as well as in relation with emerging magnetic memory and logic devices. New DW-based devices were recently proposed, for example to replace hard drive disks with higher density and faster date transfer. Moreover, in Magnetic Random Access Memory (MRAM), identified as one of the most promising candidate for DRAM and SRAM replacement, switching occurs through DW propagation. Control of current induced DW dynamics has long been a challenge mainly due to material imperfections. Only some years ago, fast and controllable motions were reported in multilayers presenting structural inversion asymmetry (SIA). More recently, a mechanism was proposed based on the presence of spin orbit torques and Dzyaloshinskii-Moriya interaction (DMI), both phenomena originating from the spin orbit interaction and needing (SIA).My initial objective was to test this model in two systems presenting different SIA. In Pt/Co/Pt multilayers with weak SIA, I studied both current and field induced DW motion and evidenced a chiral damping. This new phenomena, counterpart of the DMI for the dissipative aspects, influences both current and field induced dynamics and has to be taken into account for a complete picture of the mechanism. In Pt/Co/AlOx multilayers with strong SIA, I studied new geometries where the DW motion the and current flow are not collinear. I evidenced asymmetric DW motion as a function of this non-collinearity that cannot be explained with a simple SOT+DMI model. Based on these experimental results I introduce a new device concept named “magnetic origami”: the shape of the device governs the switching mechanism. This concept provides large flexibility to construct fast, low power non-volatile magnetic memory: different functionalities can be achieved on a wafer by simply mastering the shape of the different elements. I show the proof of concept of two such devices.