Near-infrared and far-infrared data of 10 planetary nebulae are analyzed and compared with corresponding radio data. Evidence is found for the presence of dust grains mixed with the ionized gas. The dust-to-gas mass ratio, the grain size, and the grain number density are found to vary systematically with the nebular radius. These results can be explained either as due to progressive grain fragmentation and partial destruction with time or as reflecting a higher concentration of dust grains in the inner part of the planetary nebula envelope when it was ejected from the parent star. Possible evidence and tests which may support or disprove either possibility are briefly reviewed.