Refractory metal alloys are candidates for the next generation of materials for extreme conditions, but challenges associated with their ductility, processability, and environmental resistance limit their application. Computational modeling and simulation can help understand the mechanisms underpinning these alloys' mechanical properties so they can be controlled in the future. Here, a mesoscale model, phase-field dislocation dynamics (PFDD), is extended to model the fundamental aspects of refractory alloys and used to simulate dislocation behavior in several refractory alloy systems. First, the PFDD formulation is adjusted to simulate a newer class of materials, multi-principal element alloys (MPEAs). The simulations reveal highly statistical behavior that is inherent to these random alloys. Second, a local concentration parameter is added to PFDD to simulate the effects of interstitial atoms such as oxygen and hydrogen. Both short-range and long-range interactions between interstitial atoms and dislocations are accounted for. The effect of interstitial atoms on dislocation core structures, critical glide stresses, and mobility are simulated and discussed. This work provides both new insights into dislocation behavior in refractory materials and a new mesoscale framework for simulating other alloy systems of interest.