This article provides a brief account of solution-phase methods that generate silver and gold nanostructures with well-controlled shapes. It is organized into five sections: The first section discusses the nucleation and formation of seeds from which nanostructures grow. The next two sections explain how seeds with fairly isotropic shapes can grow anisotropically into distinct morphologies. Polyol synthesis is selected as an example to illustrate this concept. Specifically, we discuss the growth of silver nanocubes (with and without truncated corners), nanowires, and triangular nanoplates. In the fourth section, we show that silver nanostructures can be transformed into hollow gold nanostructures through a galvanic replacement reaction. Examples include nanoboxes, nanocages, nanotubes (both single- and multi-walled), and nanorattles. The fifth section briefly outlines a potential medical application for gold nanocages.We conclude with some perspectives on areas for future work.