Heterogeneous or stratified waves are ubiquitous in nature. For instance, in the ocean salinity, temperature gradients, and topography have been observed to generate traveling waves, which then propagate over long distances. We will present a strong and weak existence theory for two-dimensional steady stratified waves in water, both with and without the effects of surface tension. In addition, we shall discuss some qualitative features of these waves. A portion of this work is joint with V. M. Hur.