In recent years, twisted laser beams and optical vortices have attracted considerable interest, in terms of both their fundamental quantum properties and also their potential technical applications. Here we examine what novel features might emerge from the interaction of such beams with chiral matter. In this connection we assess the possible scope for exploiting similarities between the angular momentum properties of circularly polarised light and optical vortices - both with regard to their mechanical torque and also the associated spectroscopic selection rules. Twisted beams have generally been studied only in their interactions with achiral matter, with the theory largely developed for electric dipole coupling. In chiral systems, the low symmetry enables many optical transitions to be allowed under the selection rules for both electric and magnetic multipoles, and the entanglement of spin and orbital photon angular momentum requires careful extrication. Specific issues to be addressed are: what new features, if any, can be anticipated when such beams are used to interrogate a chiral system, and whether in such cases enantiomeric specificity can be expected. To this end we develop theory that goes to a higher order of multipole expansion, also engaging magnetic dipole and electric quadrupole transitions. Finally, we study the response of nematic liquid crystal media to the throughput of twisted laser light. Specific attention is focused on the spatial evolution of the director orientation angle.