This thesis frames the topic of peristalsis due to its occurrence in biofluid mechanics and in various physiological fluid transport in living bodies. The squeezing action of muscles, transfusion of blood through pumping, primitive heart beating, coordinated contractions of ureteral walls to dispose urine, vascular motions of blood vessels, embryo pumping in tubes, locomotion of worms, myogenic cardiac enlargement, intestinal contractions, food intake to its disintegration etc involve the peristaltic pumping. The waves of constant wavelength and amplitude (periodic waves) traveling along the tube length stems the peristaltic excitation in human physiology. Keeping in mind the rhythmic and symmetrical contractions of muscles the Greek word "peristaltikos" meaning "compressing and clasping" provides basis for the word peristalsis. In addition the peristaltic movements are not limited to its natural aspect. The mechanism is equally appealing in engineering and industry. The pumping characteristic of peristalsis has key role in fabricating pumps to transport toxic liquid in order to avoid contamination of the outside environment and sanitary fluid in industrial processes. Such technique is highly advantageous in processes where the medium containing fluid is deformable under applied stresses. The captivating attributes of peristalsis find noteworthy applications in medical and industrial processes in modern industry. Ceramic, porcelain, food, paper and building industries, heart-lung machine, roller, finger and blood pumps, dialysis machines, endoscope, displacement pumps are designed on principle of peristalsis. It should be noted that beginning from esophagus to ureteral walls the whole alimentary canal is naturally configured in curved shape. Moreover motion of fluid through wave propagation mechanism in physiological conduits, glandular ducts, industrial tubes/channels, blood arterial walls and capillaries involves curved flow peristalsis. Thus straight/planar channel assumption is found inadequate in such situations. The accurate execution of such systems require curvilinear mathematical description though they lead to complicated mathematical expressions. In addition consideration of peristalsis in respiratory, blood capillaries and cardiovascular division operates in alliance with compliant wall properties. The compliance in the boundaries specify the change in volume due to pressure. In fluid flow problems this effect can be executed in terms of stiffness, elasticity and damping of peristaltic walls. On account of physiological and industrial peristalsis, the objective here is to develop and analyze the fluid flows through periodic wave transport in channels. Such considerations are focused particularly for human tubular organs functioning to inspect the outcomes of different effects. Thus the mathematical challenges are performed based on essential laws and complexity in a medium is taken with reference to peristalsis. The problems are considered by keeping natural phenomenon intact and then solved through different qualitative schemes (numerical and perturbation). Thus organization of this thesis as follows. Chapter 1 manifests the literature review based on peristaltic mechanism under different aspects and fundamental equations that will be utilized throughout the remaining chapters. Chapter 2 aims to examine the peristaltic transport of pseudoplastic fluid under the radially imposed magnetic field and convective heat and mass conditions. The channel walls in the study satisfy the wall properties. The relevant formulation is made on the basis of long wavelength approximations. The corresponding solutions are evaluated and analyzed for both planar versus curved channel. Streamlines are developed for the fluid and curvature parameters. The contents of this chapter are published in Journal of Magnetism and Magnetic Materials 403 (2016) pp 47--59. The objective of Chapter 3 is to analyze the peristaltic transport of incompressible fluids in a curved channel subject to the following interesting features. Firstly to examine the influence of non-uniform applied magnetic field in radial direction. Secondly to consider compliant walls of channel. Thirdly to analyze the curvature effect in flow of Carreau-Yasuda material. Fourth to examine the influence of heat transfer with viscous dissipation. Fifth to address the impact of velocity and thermal slip conditions. The relevant problems are formulated. Outcoming problems through lubrication approach are solved. Attention is focused to the velocity, temperature, heat transfer coefficient and streamlines. The contents of this chapter are published in AIP Advances 5, 127234 (2015) DOI: 10.1063/1.4939541. Chapter 4 describes the magnetohydrodynamic peristaltic flow of Carreau fluid in a curved channel. The flow and heat transfer are discussed in presence of wall slip and compliant conditions. The generation of fluid temperature and velocity due to viscous dissipation and gravitational efforts are recorded respectively. Moreover indicated results signify activation of velocity, temperature and heat transfer rate with Darcy number. The contents of this chapter are submitted in Journal of Mechanics. The purpose of Chapter 5 is twofold. Firstly to explore and compare the shear thinning and thickening effects in peristaltic flow of an incompressible Sisko fluid. Secondly to inspect homogeneous-heterogeneous reactions effects. Mixed convection, thermal radiation and viscous heating are present. The governing equations have been modeled and simplified using lubrication approach. The solution expressions are approximated numerically for the graphical results. The contents of this chapter are published in Journal of Molecular Liquids 233 (2017) pp 131-138. Chapter 6 models the peristaltic flow of Sisko fluid in a curved channel. Porous medium is characterized by modified Darcy''s law. Radial magnetic field is applied. Such consideration is significant to predict human physiological characteristics especially in blood flow problems. Moreover the particular features of blood flow regimes in narrow arteries and capillaries i-e., compliance and slip at the boundaries are not ignored. The whole system is set to long wavelength approximation. The detail of plotted graphs through numerical simulation is discussed. The contents of this chapter are also published in Journal of Molecular Liquids 236 (2017) pp 290-297. Chapter 7 investigates the impact of homogeneous-heterogeneous reactions in peristaltic transport of third grade fluid in a curved channel. The third grade fluid has an ability to explore shear thinning and shear thickening effects even in steady case. The channel walls in this study satisfy the wall properties. The fluid is electrically conducting in the presence of radially imposed magnetic field. The relevant formulation is made. Solutions are computed and analyzed for various parameters of interest. The main observations are summarized in the conclusions. The contents of this chapter are published in AIP Advances 5, 067172 (2015) DOI: 10.1063/1.4923396. Chapter 8 has been designed to explore the MHD characteristics of Jeffery nanofluid with wall properties in curved flow stream. Such consideration is more realistic and finds its importance in blood circulatory systems where both MHD and flexibility of walls play essential role. The impact of thermal radiation is not ignored since heating by radiation allows a greater speed and uniformity in reaching a set temperature due to characteristics of electromagnetic waves. Further the chemical reaction effect has been outlined in nanofluid flow up to first order. The nonlinear and coupled system is set to long wavelength and low Reynolds number assumption. The results are plotted numerically and physically interpreted in the last section. The contents of this chapter are published in Neural Computing and Applications (2016) DOI: 0.1007/s00521-016-2705-x pp 1-10. Chapter 9 focusses its description in curved channel flow of Jeffery fluid through modified Darcy''s law. In view of blood circulatory system the important aspect of wall flexibility is not ignored. Further the thermal radiation and wall slip are accounted in mathematical description of the problem. The chemical reaction effects are also present in nanofluid flow. The resulting complex mathematical system is solved efficiently through numerical approach. The flow behavior in terms of velocity, temperature, heat transfer rate and nano particle mass transfer have been emphasized in the discussion. The contents of this chapter are published in Journal of Molecular Liquids 224 (2016) 944-953. In Chapter 10 the description of flow saturated in porous space followed by Darcy''s observations are exploited to obtain mathematical model. Fluid flow comprising porous media in view of modified Darcy''s law is developed. Flow stream is developed for Carreau-Yasuda nanofluid in a curved channel. Effectiveness of buoyancy is executed through mixed convection. Further thermal radiation and viscous dissipation effects are included. The graphical interpretation is made through numerical solutions. The physical significance of involved parameters is pointed out in detail. The contents of this chapter are published in Plos One (2017) DOI: 10.1371/journal.pone.0170029. Chapter 11 discusses the effects of thermophoresis and Brownian motion in peristaltic flow of Eyring-Powell fluid in a curved channel. The channel boundaries are subject to no-slip and flexible/compliant properties. The thermal radiation is not ignored. Mixed convection in this analysis is also accounted. The solution expressions are approximated through numerical approach. The effects of sundry parameters on quantities of interest are illustrated physically. The contents of this chapter are published in Computers in Biology and Medicine 82 (2017) pp 71-79." xml:lang="en_US