In this book, we have analyzed the mathematical models on peristaltic flow transport of Newtonian fluid, couple stress fluid, Jeffery fluid and nanofluid through different physiological flow regimes. Couple stress fluid has been taken in first four mathematical models from Chapter-2 to Chapter-5. The dimensionless governing equations are solved for flow variables by analytical method in Chapter-2 to Chapter-5. In Chapter-1 a brief discussion of peristaltic flow transport, magnetohydrodynamics, couple stress fluids, thermal radiation and heat and mass transfer followed by a literature survey on peristaltic flow transport and identification of gaps in literature. The governing equations for the presented models are represented in partial differential equations with boundary conditions. We have simplified the governing equations by using long wavelength and low Reynolds number approximations.