Bioorthogonal chemistry has emerged as a new powerful tool that facilitates the study of structure and function of biomolecules in their native environment. A wide variety of bioorthogonal reactions that can proceed selectively and efficiently under physiologically relevant conditions are now available. The common features of these chemical reactions include: fast kinetics, tolerance to aqueous environment, high selectivity and compatibility with naturally occurring functional groups. The design and development of new chemical transformations in this direction is an important step to meet the growing demands of chemical biology. This chapter aims to introduce the reader to the field by providing an overview on general principles and strategies used in bioorthogonal chemistry. Special emphasis is given to cycloaddition reactions, namely to 1,3-dipolar cycloadditions and Diels-Alder reactions, as chemical transformations that play a predominant role in modern bioconjugation chemistry. The recent advances have established these reactions as an invaluable tool in modern bioorthogonal chemistry. The key aspects of the methodology as well as future outlooks in the field are discussed.