Engine systems and associated methods, including systems with semi- isothermal compression devices are disclosed. An engine system in accordance with a particular embodiment includes a compressor having a compressor inlet and outlet, a combustor having a combustor inlet coupled to the compressor outlet and further having a combustor outlet, a positive displacement expander having an expander inlet coupled to the combustor outlet, and further having an expander outlet and a work output device. A valve is coupled between the combustor and the expander to regulate a flow of hot combustion products passing from the combustor to the expander, and an exhaust energy recovery device is coupled to the expander outlet to extract energy from the combustion products exiting the expander.