Bacteria are single-celled microorganisms that can exist in three basic shapes - rods (called bacilli), spheres (called cocci), or spirals. They reproduce through binary fission and consume nutrients in various ways. Bacteria are classified based on several factors including their shape, staining properties, oxygen requirements, environment, and cell wall composition. Some key groups of bacteria include phototrophic bacteria, gliding bacteria, sheathed bacteria, and spirochetes.