A sharpener for blades comprises a movable blade-sharpening surface, a stationary blade guide supported closely adjacent the surface, and a movable support for a blade. The support comprises pivotally interconnected first and second links and a blade holder. The first link is pivotably supported at a location fixed with respect to the blade guide, the second link supports the blade holder adjacent a distal end of the second link. The links support the blade holder for movement in first directions toward and away from the blade-sharpening surface, in second directions transverse to the first directions, and in third directions transverse to the first and second directions. The blade holder is pivotably supported on the second link, with the links and pivots being located and ganged to support the blade holder adjacent the blade guide for movement in three substantially mutually perpendicular directions relative to the blade guide and blade-sharpening surface.