Combustion by compression of a lean and homogeneous (or premixed) air-fuel mixture has recently emerged as an effective alternative to achieve simultaneous nitrogen oxides (NOx) and particulate matter (PM) reduction in internal combustion engines. This novel process can be considered as a hybrid between the spark ignition (SI) and the compression ignition (CI) combustions. To obtain it is necessary to generate a homogeneous (or highly premixed) mixture of fuel and air (such as SI combustion), but this mixture is compressed up to its auto ignition limit (such as DI combustion). Even though this process has been identified as Homogeneous Charge Compression Ignition (HCCI), a variety of systems that use this concept have recently appeared. This document presents a review of such systems.