At present, the U.S. Fusion Engineering Systems Study (FESS) considers several cooling/breeding concepts that utilize flowing liquid metals (LMs), Li, or eutectic PbLi alloy as working fluids for implementation of these concepts in the Fusion Nuclear Science Facility (FNSF). In this paper, we review recent modeling activities aimed at the investigation of LM flows and heat transfer relevant to the FESS-FNSF program. In particular, considerations are given to (1) development and validation & verification of computational magnetohydrodynamic (MHD) codes, (2) characterization of critical coupled MHD/heat transfer phenomena, and (3) design and analysis for selected LM applications in the FNSF. Under these three research thrusts, the reviewed topics including the MHD code HyPerComp Incompressible MHD solver for Arbitrary Geometries (HIMAG), MHD mixed-convection flows, MHD pressure drop in the blanket inlet/outlet manifolds, PbLi flows in a thermal convection loop, MHD PbLi flows in a dual-coolant lead-lithium blanket prototype, and a design window for a flowing Li divertor with He-cooled substrate.