  We present a comprehensive review of physics effects generated by leptoquarks
(LQs), i.e., hypothetical particles that can turn quarks into leptons and vice
versa, of either scalar or vector nature. These considerations include
discussion of possible completions of the Standard Model that contain LQ
fields. The main focus of the review is on those LQ scenarios that are not
problematic with regard to proton stability. We accordingly concentrate on the
phenomenology of light leptoquarks that is relevant for precision experiments
and particle colliders. Important constraints on LQ interactions with matter
are derived from precision low-energy observables such as electric dipole
moments, (g-2) of charged leptons, atomic parity violation, neutral meson
mixing, Kaon, B, and D meson decays, etc. We provide a general analysis of
indirect constraints on the strength of LQ interactions with the quarks and
leptons to make statements that are as model independent as possible. We
address complementary constraints that originate from electroweak precision
measurements, top, and Higgs physics. The Higgs physics analysis we present
covers not only the most recent but also expected results from the Large Hadron
Collider (LHC). We finally discuss direct LQ searches. Current experimental
situation is summarized and self-consistency of assumptions that go into
existing accelerator-based searches is discussed. A progress in making
next-to-leading order predictions for both pair and single LQ productions at
colliders is also outlined.
