An improved resilient sanding block of the type comprising a core having a plurality of exterior surfaces, including a first major surface and a second major surface and side surfaces, and having a layer of abrasive material disposed thereon. The resilient sanding block may have one or more apertures or through holes extending from one major surface to the other major surface and channels formed in at least one of the major surfaces, with the channels in communication with the aperture. When a vacuum source is operatively connected to the aperture, the dust created by sanding will be substantially removed into the vacuum source via the channels and the aperture. A holder for a resilient sanding block is also disclosed, as well as a handle for the holder, which together form a sanding system.