The Intermediate Long Wave equation (ILW) describes long internal gravity waves in stratified fluids. Closely related to the KdV and the Benjamin-Ono equation, the ILW equation enjoys a similar well-posedness theory and is formally completely integrable. Kodama, Ablowitz and Satsuma discovered the formal integrability of ILW and formulated inverse scattering transform solutions. If made rigorous, integrability can provide powerful tools to analyze the long time dynamics of the equation. In this talk, I will give an introduction to the inverse scattering method, and present some recent results on the ILW direct scattering problem. This is joint work with Peter Perry.