ABSTRACT:  Atmospheric pressure plasmas (APPs) are partially ionized gases at the core of diverse established and emerging applications in materials processing, resource recovery, water treatment, and medicine, among others. APP processes span a wide range of power density, from low-power non-thermal to high-power thermal discharges, and typically involve interactions with electromagnetic fields, working gas streams, and confining and processing materials. These interactions lead to significant fluid dynamic-chemical-thermal-electromagnetic coupling and to distinct microscopic (kinetic) and macroscopic (dissipative) nonequilibrium phenomena. Nonequilibrium can be desirable, when exploited to achieve high process selectivity or efficiency; or detrimental, when it limits process control or uniformity. This talk will present an overview of current advances and challenges in the computational modeling and simulation of APPs, especially as they relate to unveiling novel understanding of nonequilibrium phenomena, from multiphase chemical kinetics and plasma-radiation interaction to stability, self-organization, and turbulence.