Low temperature combustion (LTC) engines are an emerging engine technology that offers an alternative to spark-ignited and diesel engines. One type of LTC engine, the homogeneous charge compression ignition (HCCI) engine, uses a well-mixed fuel–air charge like spark-ignited engines and relies on compression ignition like diesel engines. Similar to diesel engines, the use of high compression ratios and removal of the throttling valve in HCCI allow for high efficiency operation, thereby allowing lower CO2 emissions per unit of work delivered by the engine. The use of a highly diluted well-mixed fuel–air charge allows for low emissions of nitrogen oxides, soot and particulate matters, and the use of oxidation catalysts can allow low emissions of unburned hydrocarbons and carbon monoxide. As a result, HCCI offers the ability to achieve high efficiencies comparable with diesel while also allowing clean emissions while using relatively inexpensive aftertreatment technologies. HCCI is not, however, without its challenges. Traditionally, two important problems prohibiting market penetration of HCCI are 1) inability to achieve high load, and 2) difficulty in controlling combustion timing. Recent research has significantly mitigated these challenges, and thus HCCI has a promising future for automotive and power generation applications. This article begins by providing a comprehensive review of the physical phenomena governing HCCI operation, with particular emphasis on high load conditions. Emissions characteristics are then discussed, with suggestions on how to inexpensively enable low emissions of all regulated emissions. The operating limits that govern the high load conditions are discussed in detail, and finally a review of recent research which expands the high load limits of HCCI is discussed. Although this article focuses on the fundamental phenomena governing HCCI operation, it is also useful for understanding the fundamental phenomena in reactivity controlled compression ignition (RCCI), partial fuel stratification (PFS), partially premixed compression ignition, spark-assisted HCCI, and all forms of low temperature combustion (LTC).