Quasiregular maps form a higher-dimensional class of maps with many similar properties to holomorphic maps, such as continuity, openness, discreteness, and versions of the Liouville and Picard theorems. In this talk, we give a pointwise definition of quasiregularity. We show that this condition yields counterparts to many fundamental properties of quasiregular maps at a single point. The studied maps have already shown to play a key part in various important 2D results. Joint work with Ilmari Kangasniemi.