Liquid crystal elastomers (LCEs) exhibit complex thermomechanical behaviors that can be harnessed for a wide variety of applications in soft robotics, biomedical devices, and impact protection. The material comprises stiff mesogens bound in an elastomeric network of flexible polymer chains. The mesogens can order and disorder in response to temperature and mechanical deformation. This allows LCEs to undergo reversible phase transitions between the disordered isotropic, ordered monodomain, and polydomain states. The motion of the mesogens relative to the polymer network also leads to unique behaviors, including large reversible actuation response to temperature and soft elasticity. LCEs also display enhanced dissipation over conventional elastomers from the viscous rotation and ordering of the mesogens and relaxation of the network chains. The viscoelastic dissipation mechanisms can be exploited to design LCE materials and structures with extraordinary toughness, impact energy absorption, and mechanical damping. Yet, these same properties may impede the actuation and morphing capabilities of the material. Predictive modeling is needed to efficiently design and optimize LCE structures to achieve the desired performance. This presentation will describe our efforts to develop generalized continuum theories for the thermoviscoelastic behavior of monodomain nematic elastomers that describe the viscous director rotation, viscous mesogen ordering, and viscoelastic network deformation mechanisms. We specified constitutive functions for the nematic and mechanical components of the free energy density and viscosities based on experimental observations, and applied the resulting models to design energy-absorbing architected materials, evaluate the effectiveness of actuators, and optimize the director pattern of monodomain nematic elastomeric sheets to maximize viscoelastic dissipation.