This review is intended to give an overview of recent results on plasma-assisted ignition and combustion. The influence of electrical discharges on combustion processes is introduced, and the excited species and radicals present in large quantity in the plasma are detailed. A description of theoretical problems related to modeling plasma-assisted combustion is given, elucidating the role of excited states in enhancing the reaction rates. Then some experiments are reported, focused on fundamental aspects on the effects of high pressure discharges in improving the ignition of combustion. To conclude, some applications for plasma-assisted combustion and detonation are presented, activated by different kinds of discharges.