We report the development of a modular multiphysics computational framework for performing continuum simulations of low-temperature plasmas. The primary goal of this work is to discuss the features of this framework along with representative results provided as examples for a range of operating conditions and geometries. This includes plasma and plasma-dielectric systems operating in direct current, radio frequency, and microwave regimes from pressures as low as 100 mTorr to atmospheric pressure. The code has several useful features including the ability to run massively parallel simulations using arbitrary geometries, structured/unstructured meshes, choice of various models such as drift-diffusion/full-momentum at runtime, and species-dependent timesteps to name a few. The verification/validation studies presented include comparison with previously published continuum and kinetic simulations with experiments. The performance of the code is also discussed with serial and distributed memory parallel runs with scaling demonstrated up to 512 cores. The design and implementation of the code can be expected to play an important role in computational studies of low-temperature plasmas in academic and industry. As part of the dissertation research, the framework was also used to study direct current and microwave microplasmas with the goal of quantifying the accuracy of continuum simulations in comparison with fundamental kinetic simulations. These results will enable decision-making in the context of choice of simulation strategy while modeling various microplasma devices.