Properties of nanocrystals are extremely sensitive to their sizes when their sizes are smaller or of the order of the excitonic diameter due to the quantum confinement effect. The interest in this field has been concentrated basically in understanding the size-property relations of nanocrystals, for example, the pronounced variation in the bandgap of the material or the fluorescence emission properties, by tuning the sizes of the nanocrystals. Thus, the optical and electronic properties of semiconductor nanocrystals can be tailor-made to suit the needs of the specific application and hence is of immense importance. One of the major aspects necessary for the actual realization of the various applications is the ability to synthesize nanocrystals of the required size with a controlled size distribution. The growing demand to obtain such nanocrystals with the required size and controlled size distribution is met largely by the solution route synthesis of nanocrystals, that constitutes an important class of synthesis methods due to their ease of implementation and the high degree of flexibility. The main difficulty of this method is that the dependence of the average size and the size distribution of the generated particles on parameters of the reaction are not understood in detail and therefore, the optimal reaction conditions are arrived at essentially in an empirical and intuitive manner. From a fundamental point of view, understanding the growth kinetics of various nanocrystals can provide a deeper insight into the phenomena. The study of growth kinetics can be experimentally achieved by measuring the time evolution of diameter using several in-situ techniques like UV-absorption and small angle X-ray scattering. Having understood the mechanism of growth of nanocrystals, it is possible to obtain the required size of the nanocrystal using optimized synthesis conditions. The properties of these high quality nanocrystals can be further tuned by doping with a small percentage of magnetic ions. The optical and magnetic properties of these nanocrystals play an important role in the various technological applications. The first part of the thesis concentrates on the theoretical methods to study the electronic structure of semiconductor nanocrystals. The second part describes the studies performed on growth of various nanocrystal systems, both in the presence and absence of capping agents. The third part of the thesis describes the studies carried out on ZnO and doped ZnO nanocrystals, synthesized using optimal conditions that were obtained in the earlier part of the thesis. The thesis is divided into five chapters which are described below. Chapter 1 provides a brief overall perspective of various interesting properties of semiconductor nanocrystals, including various concepts relevant for the study of such systems. Chapter 2 describes experimental and theoretical methods used for the study of nanocrystals reported in this thesis. In Chapter 3 of this thesis, we report results of theoretical studies carried out on III-V and II-VI semiconductors using the tight-binding (TB) methodology. Chapter 4 presents the investigations on the growth kinetics of several nanocrystal systems. Chapter 5 presents experimental investigations carried out on undoped and various transition metal (TM) doped ZnO nanocrystals. In summary, we have performed electronic structure calculations on various nanocrystal systems, devised a novel method to obtain the size distribution from UV-absorption spectrum and studied the mechanism of growth in the presence and absence of capping agents in various II-VI semiconductors. Using the optimal conditions obtained from the growth studies, we prepare high quality ZnO nanocrystals of required size, both in free-standing and capped states and doped it with small percentages of various transition metals like Mn, Cu and Fe. We have then studied their optical and magnetic properties.