The thesis describes the study of structure and dynamics of polymers in confined geometry. We study the finite size effect on the dynamics of non glassy and glassy polymers. Systematic measurement have been performed to address the issue of the possibility of entanglement and hence reptation dynamics of the polymer segments in confinement. The confinement effect on the glassy dynamics has been studied for Langmuir monolayers as well as for polymer nanoparticle hybrid systems. Slow and heterogeneous dynamics are the underlined observed behavior for dynamics in hybrid systems. The available theories explains the slowing down of the dynamics as the system is cooled from the liquid state in terms of increasing cooperative motion of the molecules. The size of the cooperative region is predicted to grow with reducing temperature. Experiments, theories and simulation in confined dimensions have been motivated to detect this length scale of the cooperatively rearranging region. The surface and interface effects on glass transition were studied using measurements based on modulated differential scanning calorimetry and small angle X ray scattering techniques. The dynamical heterogeneity in glassy polymers were studied using advanced X ray photon correlation spectroscopy techniques. Our studies presented in this thesis are also an small step to contribute to the existing experimental results on studying the surface, interface and finite size effects on the morphology and dynamics of confined systems. These effects were studied for, firstly ultra thin Langmuir monolayers and secondly polymer nanoparticle hybrid systems. In Chapter 1, we provide the theoretical background along with brief review of the literature for understanding the results presented in this thesis. The details of the experimental set up and their operating principle along with the details of the experimental conditions are provided in Chapter 2. In Chapter 3 we presents our experimental results on surface morphology and surface dynamics in ultra thin Langmuir monolayer of polymers. Chapter 4 and Chapter 5 discusses the result based on polymer nanoparticle hybrid systems. We provide the summary of our result and the future prospective of the work in Chapter 6. In appendix we have shown the complete derivation of the equation used in Chapter 3 for understanding the surface morphology of Langmuir monoalyers on water surface. Chapter 1 provides in detail the introduction to several aspects related with the dynamics of both glassy and non glassy polymers in confinement. It starts with brief introduction to structure and dynamics of polymers in bulk. In the next section we discuss the macroscopic viscoelastic behavior of materials followed by a very brief discussion on the common techniques used for such measurement. Further it discusses the theory and several available models present in literature to understand the dynamics of glass transition. This section is followed by discussion on surface and interface effects on structure and dynamics of such systems in confinement. Towards the end of this chapter we discuss the universal behavior of slow dynamic observed in soft glassy materials. Chapter 2 contains the details of the experimental techniques which has been used for the study. Brief introduction to basic principles of the measurements followed by details of the material and methods have been provided. The surface morphology and dynamics of Langmuir monolayer of polymers confined at air water interface, under compressive mechanical strain has been discussed in Chapter 3. The results presented for surface morphology are based on the studies using the combination of in situ grazing angle incidence small angle X ray scattering and ex situ atomic force microscopy measurements on monolayers transfered on silicon substrate. The issue of the presence of reptation motion in confinement has been addressed by performing systematic measurements as a function of surface concentration and molecular weight at fixed temperature. The glassy dynamical behavior has been studied on different glassy polymer layer as a function of surface concentration and temperature. In Chapter 4 we show the glass transition behavior of polymer nanoparticle (PMMA gold) hybrid system based on thermal measurements. This chapter discusses the role of the existence of a length scale in deciding the dynamics of the glass transition temperature of polymers. The confinement effect was tuned by the variation of the inter particle spacing between the nanoparticles in the polymer matrix. It also discusses the model to understand the observed behavior of the glass transition temperature in terms of the tunability of the polymer particle interface and the effect of the interface morphology on the dynamics of glass transition temperature. Chapter 5 is about the study of dynamics of polymer nanocomposites near glass transition as a function of temperature, wave vector and volume fraction of gold nanoparticles using X ray photon correlation spectroscopy. Based on our experimental results , we provide a phase diagram for dynamics in 2D space of temperature, wave vector and volume fraction for our PMMA gold nanoparticle hybrid samples. Chapter 6 contains the summary and the future perspective of the work presented.