Knocking combustion research is crucially important because it determines engine durability, fuel consumption, and power density, as well as noise and emission performance. Current spark ignition (SI) engines suffer from both conventional knock and super-knock. Conventional knock limits raising the compression ratio to improve thermal efficiency due to end-gas auto-ignition, while super-knock limits the desired boost to improve the power density of modern gasoline engines due to detonation. Conventional combustion has been widely studied for many years. Although the basic characteristics are clear, the correlation between the knock index and fuel chemistry, pressure oscillations and heat transfer, and auto-ignition front propagation, are still in early stages of understanding. Super-knock combustion in highly boosted spark ignition engines with random pre-ignition events has been intensively studied in the past decade in both academia and industry. These works have mainly focused on the relationship between pre-ignition and super-knock, source analyses of pre-ignition, and the effects of oil/fuel properties on super-knock. The mechanism of super-knock has been recently revealed in rapid compression machines (RCM) under engine-like conditions. It was found that detonation can occur in modern internal combustion engines under high energy density conditions. Thermodynamic conditions and shock waves influence the combustion wave and detonation initiation modes. Three combustion wave modes in the end gas have been visualized as deflagration, sequential auto-ignition and detonation. The most frequently observed detonation initiation mode is shock wave reflection -induced detonation (SWRID). Compared to the effect of shock compression and negative temperature coefficient (NTC) combustion on ignition delay, shock wave reflection is the main cause of near-wall autoignition/detonation. Finally, suppression methods for conventional knock and super-knock in SI engines are reviewed, including use of exhaust gas recirculation (EGR), the injection strategy, and the integration of a high tumble- high EGR-Atkinson/Miller cycle. This paper provides deep insights into the processes occurring during knocking combustion in spark ignition engines. Furthermore, knock control strategies and combustion wave modes are summarized, and future research directions, such as turbulence-shock-reaction interaction theory, detonation suppression and utilization, and super-knock solutions, are also discussed. (C) 2017 The Authors. Published by Elsevier Ltd.