This paper surveys publications on automotive powertrain control, relating to modern GTDI (Gasoline Turbocharged Direct Injection) engines. The requirements for gasoline engines are optimising the airpath but future legislation suggests not only a finely controlled airpath but also some level of electrification. Fundamentals of controls modelling are revisited and advancements are highlighted. In particular, a modern GTDI airpath is presented based on basic building blocks (volumes, turbocharger, throttle, valves and variable cam timing or VCT) with an example of a system interaction, based on boost pressure and lambda control. Further, an advanced airpath could be considered with applications to downsizing and fuel economy. A further electrification step is reviewed which involves interactions with the airpath and requires a robust energy management strategy. Examples are taken of energy recovery and e-machine placement. Control-oriented models of gasoline engines are reviewed, and challenging control problems for conventional engines and hybrid vehicle powertrains are discussed, in particular relating to consideration of the complex interactions. A systems approach is needed to understand the attribute trade-off, with fuel consumption, emissions, as well as energy storage on a particular drive cycle. This necessitates an optimisation methodology and appropriate problem formulation of objective, states and constraints. A discussion of optimisation techniques is considered. Finally, a comprehensive list of references is provided.