Domain wall motion is in the core of many information technologies ranging from storage [Beach et al., J. Magn. Magn. Mater. 320, 1272–1281 (2008)], processing [Tatara et al., Phys. Rep. 468, 213–301 (2008)], and sensing [Ralph and Stiles, J. Magn. Magn. Mater. 320, 1190–1216 (2008)] up to novel racetrack memory architectures [Parkin et al., Science 320, 190–194 (2008)]. The finding of magnetism in two-dimensional (2D) van der Waals (vdW) materials [Huang et al., Nature 546, 270 (2017); Gong et al., Nature 546, 265–269 (2017); Guguchia et al., Sci. Adv. 4, eaat3672 (2018); Klein et al., Science 360, 1218–1222 (2018)] has offered a new frontier for the exploration and understanding of domain walls at the limit of few atom-thick layers. However, to use 2D vdW magnets for building spintronics nanodevices such as domain-wall based logic [Allwood et al., Science 309, 1688–1692 (2005); Luo et al., Nature 579, 214–218 (2020); Xu et al., Nat. Nanotechnol. 3, 97–100 (2008)], it is required to gain control of their domain wall dynamics by external driving forces such as spin-polarized currents or magnetic fields, which have so far been elusive. Here, we show that electric currents as well as magnetic fields can efficiently move domain walls in the recently discovered 2D vdW magnets CrI3 and CrBr3 at low temperatures and robust down to monolayer. We realize field- and current-driven domain wall motion with velocities up to 1020 m s−1, which are comparable to the state-of-the-art materials for domain-wall based applications [Yang et al., Nat. Nanotechnol. 10, 221–226 (2015); Woo et al., Nat. Mater. 15, 501–506 (2016); Vélez et al., Nat. Commun. 10, 4750 (2019); Siddiqui et al., Phys. Rev. Lett. 121, 057701 (2018); Ryu et al., Nat. Nanotechnol. 8, 527–533 (2013)]. Domain walls keep their coherence driven by the spin-transfer torque induced by the current and magnetic fields up to large values of about 12×109 A cm−2 and 5 T, respectively. For larger magnitudes of current or field, a transition to a hydrodynamic spin-liquid regime is observed with the emission of a periodic train of spin-wave solitons with modulational instability [Rabinovich and Trubetskov, Oscillations and Waves: In Linear and Nonlinear Systems, Mathematics and its Applications (Springer Netherlands, 2011)]. The emitted waveform achieves terahertz (THz) frequency in a wide range of fields and current densities, which opens up perspectives for reconfigurable magnonic devices. Moreover, we found that these spin-waves can transport spin angular momentum through the layers over distances as long as 10 μm without losses for the transport of spin information. Our results push the boundary of what is currently known about the dynamics of domain walls in 2D vdW ferromagnets and unveil strategies to design ultrathin, high-speed, and high-frequency spintronic devices.