Among various types of energy conversion systems, hydrogen-fueled solid oxide fuel cells (SOFCs) have been acknowledged as one of the most promising technologies, thanks to the high energy density and numerous environmental and technical benefits they offer. The current study aims to provide a comprehensive review on numerical software-based modeling of these systems. The work is motivated by the increasing demand in utilization of software packages for investigating the multi-physiochemical phenomena occurring within the cell. The available software packages are introduced with the different applications being outlined. Novelty of each work as well as the corresponding drawbacks are represented through a critical approach. In the end, innovative designs and models, existing gaps in the literature, careful considerations for developing the numerical models, and recommendations for achieving further improvements in the field are provided. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.