This workshop, sponsored by AIM and the NSF, will be devoted to the study of integrable models for dispersive Hamiltonian partial differential equations. The landscape of dispersive equations is vast in scope, touching on applications from water wave dynamics to nonlinear optics. The mathematical topics range from well-posedness theory to long-time dynamics and other asymptotic limits, in both deterministic and random scenarios. Since their discovery nearly 60 years ago, integrable equations like the Korteweg-de Vries and nonlinear Schrödinger equations have been useful as guideposts in this landscape, since integrability provides tools not otherwise available, allowing for precise results.