Semiconductor nanocrystals are tiny fluorescent particles that have recently made a major impact in the biological and medical sciences by enabling high-sensitivity imaging of biomolecules, cells, and tissues. Spherical quantum dots are the prototypical material for these applications but recent synthetic advances have led to a diverse range of nanostructures with controllable sizes, shapes, and materials combinations that offer new dimensions of optical and structural tunability. Uniform anisotropic shapes with linearly polarized light emission allow optical imaging of particle orientation, planar structures have large flexible surfaces and ultra-narrow electronic transitions, and compact nanoparticles have enhanced diffusion in crowded biological environments. These properties are providing unique opportunities to probe basic biological processes, cellular structures, and organismal physiology.