Chiral magnetic systems gain more and more relevance for future information technology. Aside from the now famous proposal of skyrmionic information bits, recent publications suggest possible applications in the field of neuromorphic computing in the form of skyrmionic reservoirs which rely on their non-linear magnetoresistance. Despite its practical importance, a general physical understanding of the electrical transport through chiral magnets is yet to be reached. Experimental studies of the Hall conductivity in chiral magnets commonly face the challenge of how to decompose the measured signal into several parts with a clear physical interpretation. Theoretical investigations on the other hand struggle with the complex electronic structure, especially in the case of isolated topological solitons. Inspired by our recent work on the orbital magnetism of chiral magnets, we demonstrate how a semiclassical gradient expansion can shed some light on the classification of Hall effects in chiral magnets. These results may open up new perspectives for the all-electrical detection of non-collinear magnetic structures such as skyrmions, hopfions and chiral bobbers.