Spintronics, utilizing both the charge and spin of electrons, benefits from the nonvolatility, low switching energy, and collective behavior of magnetization. These properties allow the development of magnetoresistive random access memories, with magnetic tunnel junctions (MTJs) playing a central role. Various spin logic concepts are also extensively explored. Among these, spin logic devices based on the motion of magnetic domain walls (DWs) enable the implementation of compact and energy-efficient logic circuits. In these devices, DW motion within a magnetic track enables spin information processing, while MTJs at the input and output serve as electrical writing and reading elements. DW logic holds promise for simplifying logic circuit complexity by performing multiple functions within a single device. Nevertheless, the demonstration of DW logic circuits with electrical writing and reading at the nanoscale is still needed to unveil their practical application potential. In this review, we discuss material advancements for high-speed DW motion, progress in DW logic devices, groundbreaking demonstrations of current-driven DW logic, and its potential for practical applications. Additionally, we discuss alternative approaches for current-free information propagation, along with challenges and prospects for the development of DW logic.