Background: Heat recovery is one of the prominent ways to save a considerable amount of conventional fossil fuel and minimize its adverse effects on the environment. The rotary heat exchanger is one of the most effective and efficient devices for heat recovery or heat exchanging purposes. It is a regenerative type of heat exchanger, which has been studied and used for many heat recovery purposes. However, regenerative thermal wheels have been mostly used as heat recovery systems in buildings. For modeling a rotary regenerator, it is very important to numerically consider all the factors involved, such as effectiveness, rotational speed, geometrical size and shape, and pressure drop (Δp). In recent times, several researchers have actively studied the rotary heat exchangers, both theoretically and experimentally. Reviews: In this paper different advances in the numerical modeling of regenerative rotary heat exchangers in relation to fluid flow and heat transfer have been discussed. Researchers have indicated that the effectiveness of the regenerative rotary heat exchanger depends on various factors including, among many others, rotational speed, rotational period and combustion power. It is reported that with the increase of periodic rotation the deviation of theoretical results from the experimental result increases. The available literature indicates that regenerative heat exchangers are having relatively more effectiveness (60-80%), compared to other heat exchangers. It is also observed that the finite difference method and finite volume methods are mostly used for discretizing the heat transfer governing equations, under some assumptions. Research also indicates that for the effectiveness calculation the ε-NTU method is the most popular and convenient.