A plate heat exchanger (PHE) is a modern, effective type of heat transfer equipment capable of increasing heat recuperation and energy efficiency. For PHEs, enhanced methods of heat transfer intensification can be further applied using the analysis and knowledge already available in the literature. A review of the main developments in the construction and exploration of PHEs and in the methods of heat transfer intensification is presented in this paper with an analysis of the main construction modifications, such as plate-and-frame, brazed and welded PHEs. The differences between these construction modifications and their influences on the thermal and hydraulic performance of PHEs are discussed. Most modern PHEs have plates with inclined corrugations on their surface that create a strong, rigid construction with multiple contact points between the plates. The methods of PHE exploration are mostly experimental studies and/or CFD modelling. The main corrugation parameters influencing PHE performance are the corrugation inclination angle in relation to the main flow direction and the corrugation aspect ratio. Optimisation of these parameters is one way to enhance PHE performance. Other methods of heat transfer enhancement, including improving the form of the plate corrugations, use of nanofluids and active methods, are considered. Future research directions are proposed, such as improving fundamental understanding, developing new corrugation shapes and optimisation methods and area and cost estimations.