This paper reviews research trends in modeling for low-carbon energy production. The focus is on two currently significant low-carbon energy processes; namely, bioenergy and post-combustion carbon capture (PCC) processes. The fundamentals of these two processes are discussed and the role of modeling and simulation tools (MSTs) is highlighted. The most popular modeling software packages are identified and their use in the literature is analyzed. Among commercially available packages, it is found that no single software package can handle all process development needs such as, configuration studies, techno-economic analysis, exergy optimization, and process integration. This review also suggests that optimal modeling results reported in literature can be viewed as optimal at the individual plant level, but sub-optimal for plant superstructure level. This review has identified key gaps pertinent to developing hybrid models that describe integrated energy production processes. ASPEN Plus is found to be dominant for modeling both bioenergy and PCC processes for both steady-state and dynamic modes respectively.