A cutting tool comprising at least one blade arranged at an axial cutting head end of a tool carrier. The tool carrier comprises a chip-removal space that receives material chips removed by the blade. In some embodiments, the blade is adjacent to a chip passage feeding into the chip-removal space, which passage is limited by a radial chip gap partially limited by the blade and from there by a first and second passage surface, the first passage surface a continuation of the chip surface of the blade, the second passage surface running at an angle and widening relative to same, and is closed and limited at least in an axial sub-section facing the cutting head end, all around by a peripheral wall as a third passage surface, wherein at least one coolant channel is formed within the peripheral wall, which is provided to guide coolant to the cutting head end.