Theoretical and phenomenological implications of R-parity violation in supersymmetric theories are discussed in the context of particle physics and cosmology. Fundamental aspects include the relation with continuous and discrete symmetries and the various allowed patterns of R-parity breaking. Recent developments on the generation of neutrino masses and mixings within different scenarios of R-parity violation are discussed. The possible contribution of Rparity-violating Yukawa couplings in processes involving virtual supersymmetric particles and the resulting constraints are reviewed. Finally, direct production of supersymmetric particles and their decays in the presence of R-parity-violating couplings is discussed together with a survey of existing constraints from collider experiments.To be submitted to Physics Reports

We present a supersymmetric standard model with three gauged Abelian symmetries, of a type commonly found in superstrings. One is anomalous, the other two are E 6 family symmetries. It has a vacuum in which only these symmetries are broken by stringy effects. It reproduces all observed quark and charged lepton Yukawa hierarchies, and the value of the Weinberg angle. It predicts three massive neutrinos, with mixing that can explain both the small angle MSW effect, and the atmospheric neutrino anomaly. The Cabibbo angle is expressed in terms of the gauge couplings at unification. It conserves R-parity, and proton decay is close to experimental bounds.

In this note we elaborate on various five dimensional contributions to the effective 4D cosmological constant in brane systems. In solutions with vanishing 5D cosmological constant we describe a non-local mechanism of cancellation of vacuum energy between the brane and the singularities. We comment on a hidden fine tuning which is implied by this observation.