Reliable electrical distribution system is the primary requirement of smart grid. Further, with the integration of intermittent renewable energy sources (RESs), reliability assessment is very vital. Various deterministic and probabilistic methods are utilized to assess the reliability of distribution system. This review study is about distribution system reliability assessment (DSRA) with and without renewable energy generation technologies such as micro grid, distributed generation, solar and wind. For that purpose, DSRA methods such as Monte Carlo simulation (MCS) and other DSRA methods are discussed. The distribution system reliability is considered by using the renewable energy generation techniques. The stochastic features of the parameters in the designing process defined the type of MCS simulation technique. These techniques are utilized to provide reliability assessment of compact system due to huge computational time associated with them. It can be restricted by restricting number of lumped equipments for a given renewable energy source. Further, numerous states can also be used to describe the arbitrariness in the renewable energy generation, because of the stochastic behavior of the resources and the mechanical degradation of the system.