In this Tutorial, we overview recent developments to break and manipulate electromagnetic nonreciprocity in two-dimensional (2D) materials without relying on magnetic fields. To this purpose, we provide a general conductivity model to describe gyrotropic metasurfaces that exhibit nonreciprocity through different physical mechanisms enabled by 2D materials, including optical pumping, drifting electrons, ferromagnetic monolayers, mechanical strain, and spatiotemporal modulation. We describe in detail the resulting systems, focusing on near-field phenomena, associated to nonreciprocal bulk and edge surface plasmon propagation, and on far-field responses, related to Faraday/Kerr rotation and optical dichroism of waves propagating in free-space. Additionally, we review and contextualize recent advancements in magnet-free nonreciprocal devices based on 2D materials, ranging from Faraday rotators and optical dichrosim, to plasmonic and photonic isolators, hyperlenses, and tunable optical traps. We conclude by providing our outlook for the future development of this technology and its potential applications in areas such as communications, sensing, wave generation, and spectroscopy, among others.