The ability to design and assemble three-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp2, sp3, sp3d, sp3d2 and sp3d3. Functionalized with DNA with single-stranded sticky ends, patches on different particles can form highly directional bonds through programmable, specific and reversible DNA hybridization. These features allow the particles to self-assemble into |[lsquo]|colloidal molecules|[rsquo]| with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials.