Wave propagation in a horizontally statified medium may be characterized by the slowness p of the waves. In ray theory the travel time curves are parameterized by the slowness p, and this dependence is exploited in modern methods of tau inversion for travel times. The complete response of a stratified medium may also be represented as a superposition of cylindrical waves of varying slowness. This representation leads to the possibility of presenting the response of the stratification in a slowness time map containing both travel time and amplitude information. Such an approach requires copious good quality data but offers advantages in interpretation. Even in the presence of lateral variations of structure, slowness methods can provide useful information.