Diesel-ignited dual-fuel (DIDF) combustion of natural gas (NG) is a promising, and immediately available strategy to improve heavy-duty compression-ignition (CI) engine performance to meet challenging and evolving emissions regulations. The DIDF concept utilizes a combination of port-injected NG and direct-injected diesel to couple the relatively low-cost and low-emissions characteristics of NG combustion with the operational and performance characteristics that have made diesel CI engines ubiquitous. This combination of fuelling strategies permits a wide range of different operating modes, which are characterized by a number of fundamental combustion mechanisms. Combustion mechanisms specific to particular modes of DIDF operation have previously been addressed, however a comprehensive conceptual description of the combustion processes and modes of DIDF operation is lacking. A clear context for specific observed phenomena and DIDF operating modes is needed to bridge and extend the conclusions of investigations in this field. That need is addressed by this investigation through experimental analysis of thermodynamic and optical measurements of a broad range of DIDF fuelling modes. A 2-litre single-cylinder CI research engine capable of both conventional and optically-accessible operation was commissioned and operated with port-injected methane (CH₄). Fuelling modes were characterized using the global equivalence ratio (φglobal =0.55—0.88) and pilot fuel ratio (Rpilot =0.06—0.61) and were performed with combinations of pilot injection timing and pressure. A novel set of criteria, which used the measured apparent heat release rate (AHRR), defined sequential stages of DIDF combustion and mapped fundamental regimes of DIDF operation in the Rpilot-φglobal space. Flame propagation, and non-flame propagation DIDF operating regimes were distinguished by an apparent lean flame propagation limit observed at a CH₄ equivalence ratio (φCH₄) equal to 0.4. Pilot injection parameters were observed to be critical to combustion and emissions processes across all operating modes except for a unique subset of operating points with Rpilot=0.06. Spatially-resolved broadband visible light and OH*-chemiluminescence measurements supported the identified operating regimes, and indicated that the conventional conceptual model of DIDF combustion is not a complete description of the DIDF combustion process for all operating modes.