Over the past two decades, research and development using various atmospheric-pressure non-equilibrium plasmas has been conducted energetically for materials synthesis, surface treatment, environmental and energy applications, plasma medicine, plasma agriculture, and other applications. Precise understanding of the physics and chemistry of atmospheric-pressure non-equilibrium plasmas is indispensable for further development of these applications. In this paper, we review progress in the simulation of atmospheric-pressure non-equilibrium plasmas, especially streamer discharges and atmospheric-pressure glow discharges as the most fundamental discharge forms, using the fluid approximation model over the last two decades, and the current understanding of the discharge evolution process. In addition, we discuss recent findings on plasma–liquid interactions obtained from simulations of atmospheric-pressure plasmas in contact with liquids.