Many biological and artificial transport channels function without direct input of metabolic energy during a transport event and without structural rearrangements involving transitions from a closed to an open state. Nevertheless, such channels are able to maintain efficient and selective transport. It has been proposed that attractive interactions between the transported molecules and the channel can increase the transport efficiency and that the selectivity of such channels can be based on the strength of the interaction of the specifically transported molecules with the channel. Herein, we study the transport through narrow channels in a framework of a general kinetic theory, which naturally incorporates multiparticle occupancy of the channel and non-single-file transport. We study how the transport efficiency and the probability of translocation through the channel are affected by interparticle interactions in the confined space inside the channel, and establish conditions for selective transport. We compare the predictions of the model with the available experimental data and find good semiquantitative agreement. Finally, we discuss applications of the theory to the design of artificial nanomolecular sieves.