I will review work in plasma physics over the last decade on extensions of fluid equations beyond the collisional Chapman-Enskog regime. These extensions have employed various closure approximatons that model effects such as collisonless phase-mixing and Landau-damping. Two approaches to deriving these models will be illustrated, by a fitting procedure or by a renormalization-like procedure (by Parker and Carati). These models can be shown to give n-pole Pade approximations to the exact linear kinetic response. We will describe some of the limitations of these fluid models, and compare with fully kinetic computational approaches, which are rapidly advancing.