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Biomedicine has recently exploited many nanotechnology platforms for the detection and treatment of disease as well as for the fundamental study of cellular biology. A prime example of these successes is the implementation of semiconductor quantum dots in a wide range of biological and medical applications, from in vitro biosensing to in vivo cancer imaging. Quantum dots are nearly spherical nanocrystals composed of semiconductor materials that can emit fluorescent light with high intensity and a strong resistance to degradation. The aim of this thesis is to understand the fundamental physics of colloidal quantum dots, to engineer their optical and structural properties for applications in biology and medicine, and to examine the interaction of these particles with biomolecules and living cells. Toward these goals, new synthetic strategies for colloidal nanocrystals have been developed, implementing a cation exchange method for independent tuning of size and fluorescence, and a bandgap engineering technique that utilizes mechanical strain imposed by coherent shell growth. In addition, stable nanocrystals have been prepared with ultrathin coatings (< 2 nm), 'amphibious' solubility, and broadly tunable bioaffinity, induced by self-assembly with polyhistidine-sequences on recombinant proteins. Finally, colloidal quantum dots have been studied in biological fluids and living cells in order to elucidate their interactions with biological systems. It was found that these interactions are strongly dependent on the size of the nanocrystal, and cytotoxic effects of these particles are largely independent of their composition of heavy metal atoms, demonstrating that the rule book for toxicology must be rewritten for nanomaterials.