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In this review, we present several variants of left–right symmetric models in the context of neutrino masses and leptogenesis. In particular, we discuss various low scale seesaw mechanisms like linear seesaw, inverse seesaw, extended seesaw and their implications to lepton number violating process like neutrinoless double beta decay. We also visit an alternative framework of left–right models with the inclusion of vector-like fermions to analyze the aspects of universal seesaw. The symmetry breaking of left–right symmetric model around few TeV scale predicts the existence of massive right-handed gauge bosons WR and ZR which might be detected at the LHC in near future. If such signals are detected at the LHC that can have severe implications for leptogenesis, a mechanism to explain the observed baryon asymmetry of the Universe. We review the implications of TeV scale left–right symmetry breaking for leptogenesis.