Most plasma discharges are generated using radio-frequency electrical sources. It is therefore not surprising that interaction of electromagnetic fields with the plasma plays a key role in defining the plasma properties. This entry focuses on multi-dimensional electromagnetic modeling of low-pressure, partially-ionized plasma discharges. Two types of plasma sources are discussed—electromagnetic wave sustained discharges and those in which electromagnetic effects are of second order. Basic equations used for fluid modeling of plasma discharges are described with particular focus on the electrical aspects of the model. Using these basic equations, the Ohmic and electron cyclotron resonance (ECR) electron heating mechanisms are discussed. The concept of skin depth is also introduced. Relying on examples from the literature, methodologies developed for multi-dimensional fluid modeling of inductively coupled plasmas, ECR plasmas and capacitively coupled discharges are described.