Abstract : This thesis presents a study of selected instrumental and astrophysical systematics, which may affect the performance of new generation of future observations of the Cosmic Microwave Background (CMB) polarization. It elaborates on their impact on the science goals of those observations and discusses techniques and approaches for their removal. Its focus is on general issues typical of entire classes of experiments, but also on specific problems as encountered in the context of a CMB B-mode experiment, POLARBEAR. The main target of the CMB polarization effort undergoing currently in the field is a detection of the primordial B-modes anisotropies --- a so far undetected signature of the inflationary theories. This would have far-reaching impact on our understanding of the universe but also fundamental laws of physics. Understanding, modelling, and ultimately removal of the systematics are essential steps in any modern CMB analysis pipeline and their successful accomplishment, together with a high instrumental sensitivity, will decide of a final success of the entire effort. In this thesis I first describe optics of typical CMB experiments and introduce a parametrization of instrumental and cross-polarization effects particularly convenient for the analysis of their impact. Second, I present a model describing the atmospheric contamination and use it to provide some insights about the atmosphere's role and its impact on performance of ground-based experiments. I also outline how it could be used further to improve control of atmospheric effects in the CMB data analysis. Then, I discuss another source of sky systematics --- the polarized astrophysical foregrounds. In this context I present on the one hand a new approach to forecasting performance of the future experiments, which accounts for the presence of the foregrounds, while on the other I propose a framework for optimizing hardware of such experiments to let them achieve better performance. This part of thesis stems from a common work with drs. F. Stivoli and R. Stompor. I finally present one of the leading CMB polarization experiment POLARBEAR, in which I have been involved in over the course of my PhD studies. I describe its current status and performance as well as selected steps of its data analysis pipeline. In particular, I show methods to estimate some of the parameters introduced for the systematics modeling from simulated data. This work has been performed in collaboration with members of the POLARBEAR team.