CPV modules include a back plate having an array of 1 mm2 or smaller solar cells thereon. A backplane interconnect network is also provided on the back plate. This backplane interconnect network operates to electrically connect the array of solar cells together. A front plate, which is spaced-apart from the back plate, is provided. This front plate includes an array of primary lenses thereon that face the array of solar cells. The front plate can be configured to provide a greater than 1000× lens-to-cell light concentration to the array of solar cells. To achieve this 1000× lens-to-cell light concentration, the primary lenses can be configured as plano-convex lenses having a lens sag of less than about 4 mm. An array of secondary optical elements may also be provided, which extend between the array of primary lenses and the array of solar cells.