With growing concerns over greenhouse gas emission, novel combustion technologies are timely and critical. Fossil fuels will continue to contribute a large fraction of energy production in the near and intermediate future, making carbon capture and storage an important part of the solution. System studies show that oxy-combustion can play an important role in capturing CO2 efficiently when applied to power systems, because its efficiency and electricity prices are competitive with other low carbon energy. Gas-phase oxy-combustion, diluted with CO2 to control the flame temperature, utilizes conventional “off-the-shelve” technology. However, the combustion process exhibits characteristics different than those of air combustion because of the chemical activity of CO2, which impacts the combustor design. We summarize these characteristics. It also suffers from an energy penalty associated air separation. Alternative oxygen production technologies includes ion-transport membranes, and chemical looping using metal oxides as oxygen carriers. These technologies, while still under development, can couple oxygen separation and combustion in one process, i.e., process intensification. While an extensive knowledge base exists for gas phase oxy-combustion, these alternative technologies that rely on surface and electrochemical processes are still in their early stages. We review some fundamentals related to defect chemistry, surface and electrochemical reaction models, and their coupling with internal diffusion and external heat and mass transport, the associated rate-limiting steps and how they impact reactor design and performance. The discussion is used to explain the choice of oxygen carriers for chemical looping, and different reactor designs are summarized. Recent progress in material synthesis and chemistry show promising trends especially using perovskites, mixed oxides and dual-phase materials, and asymmetric structures for membranes and oxygen carriers. ITMs and CLC are dual-use technologies as they lend themselves naturally to water and CO2 splitting and the production of fuels and chemicals, but different materials and reactors are needed. They also present opportunities to integrate/hybridize fossil fuel systems with alternative energy sources for power and fuel production.