The thesis describes the study of slow dynamics of confined polymers and soft colloids. We study the finite size effect on the dynamics of glassy polymers using newly developed interfacial microrheology technique. Systematic measurement have been performed to address the issue of reduction of glass transition under confinements. Slow and heterogeneous dynamics are the underlined observed behavior for dynamics in confined glassy polymers. The slow relaxation dynamics and dynamical heterogeneity in polymer grafted nanoparticles (PGNPs) systems were studied using advanced X - ray photon correlation spectroscopy (XPCS) techniques. Our studies presented in this thesis on dynamics of polymer grafted nanoparticle systems in melts and solution are the first attempt to study them experimentally. Thus our work shed the light about new technique to study confined system more accurately and explore new soft colloidal system to study fascinating dynamics and interesting phase behavior. 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 present our newly developed technique (interfacial microrhelogy) and its consequences to study the complex fluids at interface. Chapter 4 discusses the concentration and temperature dependent glassy dynamics in confined glassy polymers. In Chapter 5 we provide the structural and dynamical study of polymer grafted nanoparticles in melts and solutions. We provide the summary of our result and the future prospective of the work in Chapter 6. Chapter-1 provides the ground work and theoretical aspects for understanding the results presented in this thesis. It starts with the discussion about the slow dynamics of complex fluids and transit to dynamic behavior of polymer in confinement, glassy dynamics in confinements . This also discusses the basic aspects of studying viscoelastic properties using rheology, interface rheology, microrheology, interface microrheology techinques. In continuation it discusses structure and dynamics of different soft colloids investigated for last decade and then theoretical aspects of XPCS is discussed. Towards the end of this Chapter, we discuss the procedure to explain and understand systems dynamical heterogeneity near glass like phase transition. Chapter-2 contains the details of the experimental techniques which has been used for the study of confined polymers and soft colloids. Brief introduction to basic principles of the measurements followed by details of the material and methods have been provided. Chapter-3 we discuss the interafacial microrheology of different complex fluids and advantages of the techniques is discussed in Chapter 3. This includes discussion about the technique sensitivity at the surface using quantum dots (QDs) as a probe and about the configuration of the QDs at/on monolayer. Later on establishment of the technique has been demonstrated through easurements on arachidic acid, poly(methylmethacrylate) (PMMA), poly(vinylacetate) (PVAc), poly(methylacrylate) (PMA) monolayers. The extracted subdiffusive nature of QDs in on monolayers through mean square displacement has been explained using fractional Brownian motion model. Towards the end of the chapter we discuss about the extraction of real and imaginary elastic modulus from mean square displacement data using generalized Stokes-Einstein relation for the quasi two dimensional systems and explains about the possible viscoelastic transition in the different monolayers. The concentration and temperature dependent glassy dynamics of confined polymers (PMMA) are discussed in Chapter-4. We demonstrate the microscopic nature of spatio-temporal variation of dynamics of glassy polymers confined to a monolayer of 2 3 nm thickness as a function of surface density and temperature. It illustrates the systems dynamical heterogeneity and explain the observed large reduction of glass transition temperature in confined system through finite size effect. In Chapter 5 we discuss the result based on systematic studies of dynamics of PGNPs in melts and solutions. In addition it also illustrates the structural anisotropy and anomalous dynamical transitions in binary mixture of PGNPs and homopolymers in good solvent condition. It provides temperature and wave vector dependent XPCS measurements on polymer grafted nanoparticles with the variation of functionality. The functionality ( f ) dependent nonmonotonic relaxation in melts of PGNPs and solvent quality dependent non monotonic relaxation of PGNPs system have been elaborated in the continuation. We present possible phase behavior of PGNPs system in good solvent with addition of homopolymer of two different molecular weight. Chapter 6 contains the summary and the future perspective of the work presented.