The formation of biaxial nematic phases in mixtures of surfactants and water is discussed. Emphasis is given to experimental data that confirm the existence of a biaxial nematic phase. Some new microscopic observations and birefringence measurements are reported. Biaxial nematic phases were observed in two systems that have, in addition, two uniaxial nematic phases. The general features of the phase transitions involving these nematic phases are theoretically analyzed on the basis of a Landau expansion. Specific relations for the order parameters are derived that compare favorably with the experimental results.