An overview of recent developments, trends and challenges in the synthesis, design and operation optimization of energy systems is presented in this manuscript. The static and dynamic optimization problems are stated mathematically, solution methods are mentioned in brief and classification of optimization problems based on the presence and treatment of time is presented. Examples of objective functions in single-objective optimization are given and the need for multi-objective optimization is highlighted. Special reference is made to Prof. Szargut's early statement about the need for optimization with ecological concerns. Emphasis is given to optimal synthesis of energy systems, a subject that is still between (or combines) art and science/technology. Furthermore, it is interesting to note that optimization is applied also during the development of models of systems. Hints are given on further considerations and research needs in subjects such as global optimization, as well as optimization with uncertainty, reliability, maintenance and social aspects. Examples of algorithms appearing in recent publications are given as an indication of the related strong activity. The manuscript closes with general remarks and a rather comprehensive, even though not exhaustive, list of references. (C) 2018 Elsevier Ltd. All rights reserved.