An apparatus for grinding rotary blades, in particular scythe-like blades or circular blades, in particular for machines for slicing food products, comprising: at least one mount for a rotary blade to which the rotary blade can be attached; and at least one grinding tool, wherein the grinding tool and the rotary blade attached in the mount are movable relative to one another such that a blade edge extending at the periphery of the rotary blade can be ground by the grinding tool, wherein a pivot device is provided for the grinding tool, wherein the pivot device is configured such that the grinding tool is pivotable about a pivot axis which extends through a grinding point at which the blade edge and the grinding tool contact one another during the grinding process, and wherein the pivot device has at least one pivot bearing and the axis of rotation of the pivot bearing coincides with the pivot axis of the grinding tool, characterized in that the grinding tool has a grinding wheel which contacts the blade edge at the grinding point and is pivotable about the pivot axis, with the grinding tool having a dressing wheel which forms at least approximately a V-shaped receiver for the rotary blade together with the grinding wheel and contacts the blade edge at a dressing point, with the dressing wheel being pivotable about the pivot axis together with the grinding wheel and/or independently of the grinding wheel; and in that the grinding wheel and the dressing wheel are each attached to a pivot arm (37, 39), with both pivot arms (37, 39) being attached to the pivot bearing and being rotatable about the common axis of rotation of the pivot bearing for the common pivoting of the grinding wheel and the dressing wheel, and/or with each pivot arm (37, 39) being rotatable about the common axis of rotation of the pivot bearing independently of the respective other pivot arm (37, 39) for pivoting the grinding wheel or the dressing wheel independently of the respective other wheel (29, 31). at least one mount for a rotary blade to which the rotary blade can be attached; and at least one grinding tool, wherein the grinding tool and the rotary blade attached in the mount are movable relative to one another such that a blade edge extending at the periphery of the rotary blade can be ground by the grinding tool, wherein a pivot device is provided for the grinding tool, wherein the pivot device is configured such that the grinding tool is pivotable about a pivot axis which extends through a grinding point at which the blade edge and the grinding tool contact one another during the grinding process, and wherein the pivot device has at least one pivot bearing and the axis of rotation of the pivot bearing coincides with the pivot axis of the grinding tool, characterized in that the grinding tool has a grinding wheel which contacts the blade edge at the grinding point and is pivotable about the pivot axis, with the grinding tool having a dressing wheel which forms at least approximately a V-shaped receiver for the rotary blade together with the grinding wheel and contacts the blade edge at a dressing point, with the dressing wheel being pivotable about the pivot axis together with the grinding wheel and/or independently of the grinding wheel; and in that the grinding wheel and the dressing wheel are each attached to a pivot arm (37, 39), with both pivot arms (37, 39) being attached to the pivot bearing and being rotatable about the common axis of rotation of the pivot bearing for the common pivoting of the grinding wheel and the dressing wheel, and/or with each pivot arm (37, 39) being rotatable about the common axis of rotation of the pivot bearing independently of the respective other pivot arm (37, 39) for pivoting the grinding wheel or the dressing wheel independently of the respective other wheel (29, 31).