The CLIC (Compact Linear Collider), as future linear collider, requires an intense positron source. A brief history is given up to the present baseline configuration which assumes unpolarized beams. A conventional scheme, with a single tungsten target as source of e-e+ pairs, has been studied several years ago. But, in order to reduce the beam energy deposition on the e+ target converter, a double-target system has been studied and proposed as baseline for CLIC. With this "hybrid target", the positron production scheme is based on the channeling process. A 5 GeV electron beam impinges on a thin crystal tungsten target aligned along its <111> axis, enhancing the photon production by channeling radiation. A large number of photons are sent to a thick amorphous tungsten target, generating large number of e-e+ pairs, while the charged particles are bent away, reducing the deposited energy and the PEDD (Peak Energy Deposition Density). The targets parameters are optimized for the positron production. Polarized positron beams are an option for CLIC, which needs R&D. Some brilliant positron sources are briefly reviewed.