ABSTRACT: We reviewed the literature focusing on nineteen integrated Energy System Models (ESMs) to: (i) identify the capabilities and shortcomings of current ESMs to analyze adequately the transition towards a low-carbon energy system; (ii) assess the performance of the selected models by means of the derived criteria, and (iii) discuss some potential solutions to address the ESM gaps. This paper delivers three main outcomes. First, we identify key criteria for analyzing current ESMs and we describe seven current and future low-carbon energy system modeling challenges: the increasing need for flexibility, further electrification, emergence of new technologies, technological learning and efficiency improvements, decentralization, macroeconomic interactions, and the role of social behavior in the energy system transition. These criteria are then translated into required modeling capabilities such as the need for hourly temporal resolution, sectoral coupling technologies (e.g., P2X), technological learning, flexibility technologies, stakeholder behavior, cross border trade, and linking with macroeconomic models. Second, a Multi-Criteria Analysis (MCA) is used as a framework to identify modeling gaps while clarifying high modeling capabilities of MARKAL, TIMES, REMix, PRIMES, and METIS. Third, to bridge major energy modeling gaps, two conceptual modeling suites are suggested, based on both optimization and simulation methodologies, in which the integrated ESM is hard-linked with a regional model and an energy market model and soft-linked with a macroeconomic model.