This work is a study exploring the extent of suitability of static first-principles calculations for studying diffusion in metallic systems. Specifically, vacancy-mediated volume diffusion in pure elements and alloys with dilute concentration of impurities is studied. A novel procedure is discovered for predicting diffusion coefficients that overcomes the shortcomings of the well-known transition state theory, by Vineyard. The procedure that evolves from Eyring's reaction rate theory yields accurate diffusivity results that include anharmonic effects within the quasi-harmonic approximation. Alongside, the procedure is straightforward in its application within the conventional harmonic approximation, from the results of static first-principles calculations. To prove the extensibility of the procedure, diffusivities have been computed for a variety of systems. Over a wide temperature range, the calculated self-diffusion and impurity diffusion coefficients using local density approximation (LDA) of density functional theory (DFT) are seen to be in excellent match with experimental data. Self-diffusion coefficients have been calculated for: (i) fcc Al, Cu, Ni and Ag (ii) bcc W and Mo (v) hcp Mg, Ti and Zn. Impurity diffusion coefficients have been computed for: (i) Mg, Si, Cu, Li, Ag, Mo and 3d transition elements in fcc Al (ii) Mo, Ta in bcc W and Nb, Ta and W in bcc Mo (iii) Sn and Cd in hcp Mg and Al in hcp Ti. It is also an observation from this work, that LDA does not require surface correction for yielding energetics of vacancy-containing system in good comparison with experiments, unlike generalized gradient approximation (GGA). It is known that first-principles' energy minimization procedures based on electronic interactions are suited for metallic systems wherein the valence electrons are freely moving. In this thesis, research has been extended to study suitability of first-principles calculations within LDA/GGA including the localization parameter U, for Al system with transition metal solutes, in which charges are known to localize around the transition metal element. U parameter is determined from matching the diffusivities of 3d transition metal impurity in aluminum with reliable experimental data. The effort yielded activation energies in systematic agreement with experiments and has proved useful in obtaining insights into the complex interactions in these systems. Besides the prediction of diffusion coefficients, this research has been helpful in understanding the physics underlying diffusion. Within the scope of observations from the systems studied, certain diffusion related aspects that have been clarified are: (i) cause for non-Arrnenius' nature of diffusion plots (ii) definitions of atom migration properties (iii) magnitude and sign of diffusion parameters enthalpy and entropy of formation and migration and characteristic vibrational frequency (iv) trends in diffusivities based on activation energy and diffusion prefactor (vi) cause for anomalous diffusion behavior of 3d transition metals in Al, and their magnetic nature (vii) contributions from electronic contributions to curvature at very high temperatures of bcc refractory elements (viii) temperature dependence of impurity diffusion correlation factors. Finally, the double-well potential of diffusion by vacancy mechanism has been calculated from first-principles. This aided calculation of entropy of migration and thus free energy of migration along with characteristic vibrational frequency. Also for the first time, temperature dependence of enthalpy of migration and thus atom jump frequency has been accurately predicted. From the broad perspective of...