Although there is widespread recognition that near-field (Fresnel) diffraction can occur with laser light, this fact seems not to have led to previous systematic study of near-field diffraction at simple apertures. Near-field diffraction at circular apertures is studied in detail. The number of Fresnel zones present in the diffraction pattern is given byn = ca2/λX, whereais the radius of the circle,λis the wavelength,Xis the distance from the aperture, andcis a numerical factor which is unity for collimated light, less than unity convergent light, and greater than unity for divergent light. The near-field beam for collimated light diverges noticeably only forλX/a2 > 0.25and reaches the far-field divergence forλX/a2 > 0.7. Several practical applications of near-field diffraction are suggested.