In the absence of dissipation, relativistic fluid dynamics is described by a five-field theory, namely, in terms of three velocity and two thermodynamic variables that are governed by the Euler system, five partial differential equations that determine the spatiotemporal evolution of these five fields from general initial data. Regarding the modeling of dissipation, i.e., viscosity and heat conduction, various theories have been suggested over the last almost eight decades. This talk deals with the question whether dissipative relativistic fluid dynamics can be properly modeled by a causal five-field theory, in which dissipation is described by additional terms that are linear in the gradients of the fields ("relativistic Navier-Stoke"). The question is answered in the affirmative. The proposed formulation is intimately related to the Hughes-Kato-Marsden theory of second-order symmetric hyperbolic systems on the one hand, and to the classical (non-causal) descriptions given by Eckart and Landau on the other. Joint work with Blake Temple.