This work summarizes selected applications of artificial neural networks and related solutions such as neuro-fuzzy within different control loops such as the network predictive control regarding energy saving. It also shows such applications in the chemical industry and points out why further research on these applications regarding the control of distillation columns might be economically promising, as the world market in the chemical industry is expected to grow from 3.47 trillion euro in 2017 to about 6.6 trillion euro in 2030, the energy consumption might also rise. As not only companies in the chemical industry set up energy saving programs to reduce energy consumption and greenhouse gases, the consumption of energy decreased since 1990 in Europe. Compared to other countries like China, the energy prices in Europe-especially in Germany-have the highest prices due to taxes and governmental issues. Thus, research about applications with artificial intelligence in energy saving holds the promise of economic gain.