A survey is given on the appearance of secondary instability in shear flows. The mixing layer, the flat-plate boundary layer, and plane Poiseuille flow are considered as prototype flows. The computational and analytical work which produced conceptual enlightenment is discussed. A theory of secondary instability is presented the almost periodic flow that develops in the presence of finite-amplitude traveling waves is used as a basic flow for a linear stability analysis with respect to spanwise periodic, three-dimensional disturbances. The Hill-type stability equations with periodic coefficients allow for various classes of normal modes that are associated with different types of resonance. A numerical method for solving the secondary stability problem is discussed. Results for fundamental and subharmonic modes in plane Poiseuille flow are reviewed briefly. The present scope of the theory and its potential for future extensions are discussed.