Based on recent research within optically accessible engines and combustion chambers, conceptual models for low-temperature combustion (LTC) diesel engines are proposed. To provide a reference to which the LTC conceptual models may be compared, an established conceptual model framework for conventional diesel combustion is first reviewed and updated. Then, based on multiple optical diagnostic observations and homogeneous reactor simulations using detailed chemical kinetic mechanisms, extensions to the existing conceptual model are proposed. The LTC conceptual models are not intended to describe all LTC strategies, but rather a common subset of low-load, single-injection, partially pre-mixed compression ignition conditions that are diluted by exhaust-gas recirculation to oxygen concentrations in the range of 10-15%. The models describe the spray formation, vaporization, mixing, ignition, and pollutant formation and destruction mechanisms that are consistent with experimental observations and modeling predictions for LTC diesel engines. Two separate subcategories are offered for either heavy-duty, large-bore or for light-duty, small-bore engines. Relative to the existing conventional diesel conceptual model, the features of the LTC conceptual models include longer liquid-fuel penetration, an extended ignition delay that allows more premixing of fuel, a more distinct and temporally extended two-stage ignition, more spatially uniform second-stage ignition, reduced and altered soot formation regions, and increased overmixing leading to incomplete combustion. (C) 2013 Elsevier Ltd. All rights reserved.