Chiral spintronics is a promising new branch of quantum electronics based on spin transport phenomena in materials with chiral symmetry. This review focuses on the development of chiral spintronics in helimagnets, materials characterized by a helical magnetic structure. The paper considers the general principles for describing electric and spin transport in conducting crystals in the presence of inhomogeneities in an external magnetic field and/or internal magnetic fields of exchange origin. It is demonstrated that the interaction of conduction electron spins with a spatially inhomogeneous exchange field in helimagnets provides a natural explanation for two experimentally observed spin-transport effects: the electrical magnetochiral effect and the kinetic magnetoelectric effect. An original technique for ascertaining the magnetic chirality of conductive helimagnets based on experimental studies of the aforementioned galvanomagnetic effects is presented. Constructing a theory of the spin-transfer torque effect in conductive chiral helimagnets is described, including an exploration of the influence of this effect on the magnetization and electrical resistance of helimagnets. The spin-transfer torque effect in helimagnets is demonstrated to cause rotation of the magnetization helix under the influence of an electric current. This can be used to create new devices of spin electronics in which conductive helimagnets will serve as the main functional components.