The exergy analysis is a powerful tool for investigating thermodynamic irreversibilities and to identify pathways for improving efficiencies of energy systems, including internal combustion (IC) engines. The present study provides a two-pronged methodology to increase the work output and FCEs of IC engines. First, a detailed exergy analysis of in-cylinder phenomena in an IC engine of in-cylinder phenomena was developed and performed in an IC engine operating on an advanced combustion strategy (i.e., diesel-ignited methane dual fuel low temperature combustion (LTC). Second, a combined, experimentally driven, computational exergy analysis methodology of exhaust flows to characterize crank angle-resolved exhaust exergy was introduce and implemented on a diesel engine. In this regard, an exergy analysis framework is developed to quantify in-cylinder exergy transformations in IC engines. Then, a previously validated zero dimensional, multi zone thermodynamic model of diesel-methane dual fuel LTC is used to conduct exergy analysis, study variation of exergy components and investigate the effect of operating conditions on in-cylinder exergy distribution and irreversibilities. Also, application of exergy analysis is explained and implemented for IC engines, considering exhaust waste energy recovery systems for maximizing the overall work output. Furthermore, an important existing knowledge gap by introducing a methodology for performing crank angle-resolved exergy analysis of exhaust flows from the perspective of exhaust waste energy recovery in diesel engines. The crank angle-resolved specific exergy and its thermal and mechanical components are calculated by combining experimental crank angle-resolved exhaust manifold pressure measurements with 1D system-level (GT-POWER) simulations. Moreover, the effect of exhaust back-pressure on crank angle-resolved exhaust exergy has been investigated at different back pressures for conventional diesel combustion. Additionally, exhaust flow specific exergies in the different phases of the exhaust process, the total exergy flow rates, and cumulative (time-integrated) exergy were quantified. Finally, cyclic variations in magnitudes of maximum measured exhaust pressure, calculated exhaust temperature and phasing of exhaust flow were analyzed. Also, cyclic variability in exhaust exergy components, i.e., thermal and mechanical exergies with the perspective of exhaust WER systems were investigated.