Interfacing inorganic nanoparticles and biological systems with the aim of developing novel imaging and sensing platforms has generated great interest and much activity. However, the effectiveness of this approach hinges on the ability of the surface ligands to promote water-dispersion of the nanoparticles with long term colloidal stability in buffer media. These surface ligands protect the nanostructures from the harsh biological environment, while allowing coupling to target molecules, which can be biological in nature (e.g., proteins and peptides) or exhibit specific photo-physical characteristics (e.g., a dye or a redox-active molecule). Amphiphilic block polymers have provided researchers with versatile molecular platforms with tunable size, composition and chemical properties. Hence, several groups have developed a wide range of polymers as ligands or micelle capsules to promote the transfer of a variety of inorganic nanomaterials to buffer media (including magnetic nanoparticles and semiconductor nanocrystals) and render them biocompatible. In this review, we first summarize the established synthetic routes to grow high quality nanocrystals of semiconductors, metals and metal oxides. We then provide a critical evaluation of the recent developments in the design, optimization and use of various amphiphilic copolymers to surface functionalize the above nanocrystals, along with the strategies used to conjugate them to target biomolecules. We finally conclude by providing a summary of the most promising applications of these polymer-coated inorganic platforms in sensor design, and imaging of cells and tissues.