In this article, we report the results of our detailed investigations of the growth kinetics of zero-dimensional nanocrystals as well as one-dimensional nanorods by the combined use of small angel X-ray scattering (SAXS), transmissipon electron microscopy (TEM) along with other physical techniques. The study includes growth kinetics of gold nanocrystals formed by the reduction of HAuCl4 by tetrakis(hydroxymethyl) phosphonium chloride in aqueous solution, of CdSe nanocrystals formed by the reaction of cadmium stearate and selenium under solvothermal conditions, and of ZnO nanorods formed by the reaction of zinc acetate with sodium hydroxide under solvothermal conditions in the absence and presence of capping agents. The growth of gold nanocrystals does not follow the diffusion-limited Ostwald ripening, and instead follows a Sigmoidal rate curve. The heat change associated with the growth determined by isothermal titration calorimetry is about 10 kcal·mol-1 per 1 nm increase in the diameter of the nanocrystals. In the case of CdSe nanocrystals also, the growth mechanism deviates from diffusion-limited growth and follows a combined model containing both diffusion and surface reaction terms. Our study of the growth kinetics of uncapped and poly(vinyl pyrollidone) (PVP)-capped ZnO nanorods has yielded interesting insights. We observe small nanocrystals next to the ZnO nanorods after a lapse of time in addition to periodic focusing and defocusing of the width of the length distribution. These observations lend support to the diffusion-limited growth model for the growth of uncapped ZnO nanorods. Accordingly, the time dependence on the length of uncapped nanorods follows the L3 law as required for diffusion-limited Ostwald ripening. The PVP-capped nanorods, however, show a time dependence, which is best described by a combination of diffusion (L3) and surface reaction (L2) terms.