High flow rate catheters, and related methods, are useful in dialysis and other procedures. A catheter according to the invention comprises a hub and a generally elongated conduit. The conduit has a substantially continuous and smooth wall. The conduit also defines at least one lumen and has a length extending from a proximal end to a distal end of the conduit. The proximal end is coupled to a hub and the distal end has an opening in communication with the lumen. The conduit has a conical shape which tapers along the length.