After more than one century from its first use for electric power production, steam cycles are still the object of continuous research and development efforts worldwide. Indeed, owing to its favorable thermodynamic properties, steam cycles are not only used in coal-fired power plants but in a large variety of applications such as combined cycles, concentrated solar power plants and polygeneration plants. On the other hand, to cope with the efficiency and flexibility requirements set by today’s energy markets, the design and the operation of steam cycles must be carefully optimized. A key rule is played by the simulation and optimization codes developed in the last 30 years. This paper provides an introduction to the main types of simulation and optimization problems (design, off-design operation and dynamic), an overview of the mathematical background (possible solution approaches, numerical methods and available software), and a review of the main scientific contributions.