Dynamic Nuclear Polarization (DNP) is currently one of the most efficient ways of enhancing sensitivity in solid-state Nuclear Magnetic Resonance (NMR) experiments. The DNP protocol consists in doping a sample with a small amount of paramagnetic species, typically nitroxide biradicals, and carrying out either a magic-angle spinning (MAS) solid-state NMR experiment under microwave irradiation at 100 K or a dissolution DNP (dDNP) experiment under microwave irradiation at around 1.2 K. Maximum theoretical enhancements that can be achieved in MAS DNP reach 658, while polarizations close to unity can be achieved in dDNP, translating into the possibility of studying atomic-level composition of dilute surface species at picomolar concentrations that would be otherwise out of reach. Recent years witnessed very fast development of DNP instrumentation (high-power and high-frequency microwave sources, higher magnetic fields, faster sample spinning), polarizing agents (rigid dinitroxide biradicals) and new sample preparation techniques (sample formulation, optimisation of proton and radical concentration) which brought sensitivity enhancements (in MAS DNP) and nuclear polarizations (in dDNP) close to their theoretical maximum. The first chapter of this thesis is focusing on the microscopic description of a DNP system. We show how nuclear polarization is intrinsically limited in NMR, how it can be increased, and how the introduction of paramagnetic species modifies the behaviours of various parameters in the system. In particular, we look at the spatial dependence of relaxation times, spin diffusion coefficient, and paramagnetic quenching close to the paramagnet location. The second chapter is showing how using finite element numerical simulations can simulate the propagation of magnetization in homogeneous and heterogeneous DNP systems. We show that polarizing and relaxing powers are important parameters that greatly influence polarization dynamics. We observe how the diffusion equation behaves at steady state and how it can be linked to domain sizes in heterogeneous systems. In the third chapter, experimental measurements are performed and compared with numerical simulations in order to confirm the structure of homogeneous DNP systems. The importance of radical and proton concentration are highlighted, as well as several ways of increasing the efficiency of cross polarization in homogeneous frozen solutions. Finally, heterogeneous systems are studied in chapter four, where we combined NMR experiments and numerical simulations to determine spin diffusion coefficients, domain sizes, structures of core-shell particles, structure of perovskite materials, and predict that the bulk of inorganic materials can be significantly enhanced by DNP using spin diffusion.