A downhole cutting tool which may be a reamer or a mill has a rotary tool body with at least one block which carries hard-faced cutters and projects or is extensible from the tool body. A radially outward facing part of the cutter block defines a channel for fluid flow which extends generally axially along the cutter block. The channel is configured such that at least the rotationally trailing edge of the channel extends along the block in one or more directions which are inclined relative to the tool axis. This reduces or avoids the amount of channel edge parallel to the tool axis and thereby mitigates whirling and/or or vibration.