This paper reviews recent efforts to realize a high-efficiency memory for optical pulses using slow and stored light based on electromagnetically induced transparency (EIT) in ensembles of warm atoms in vapor cells. After a brief summary of basic continuous-wave and dynamic EIT properties, studies using weak classical signal pulses in optically dense coherent media are discussed, including optimization strategies for stored light efficiency and pulse-shape control, and modification of EIT and slow/stored light spectral properties due to atomic motion. Quantum memory demonstrations using both single photons and pulses of squeezed light are then reviewed. Finally a brief comparison with other approaches is presented.