Positron sources are the key elements for the future and
current lepton collider projects such as ILC, CLIC, SuperKEKB,
FCC-ee, Muon Collider/LEMMA, etc., introducing challenging critical
requirements for high intensity and low emittance beams in order to
achieve high luminosity. In fact, due to their large production
emittance and constraints given by the target thermal load, the main
collider parameters such as the peak and average current, the
emittances, the damping time, the repetition frequency and
consequently the luminosity are determined by the positron beam
characteristics. In this paper, the conventional positron sources
and their main properties are explored for giving an indication to
the challenges that apply during the design of the advanced
accelerator concepts. The photon-driven positron sources as the
novel approach proposed, primarily for the future linear colliders,
are described highlighting their variety and problematic.