The focus of this review is the presentation of the most important aspects of chemical bonding in molecules of the main group atoms according to the current state of knowledge. Special attention is given to the difference between the physical mechanism of covalent bond formation and its description with chemical bonding models, which are often confused. This is partly due to historical reasons, since until the development of quantum theory there was no physical basis for understanding the chemical bond. In the absence of such a basis, chemists developed heuristic models that proved extremely valuable for understanding and predicting experimental studies. The great success of these simple models and the associated rules led to the fact that the model conceptions were regarded as real images of physical reality. The complicated world of quantum theory, which eludes human imagination, made it difficult to link heuristic models of chemical bonding with quantum chemical knowledge. In the early days of quantum chemistry, some suggestions were made which have since proved untenable. In recent decades, there has been a stormy development of quantum chemical methods, which are not limited to the quantitative accuracy of the calculated properties. Also, methods have been developed where the experimentally developed models can be quantitatively expressed and visually represented using mathematically well-defined terms that are derived from quantum chemical calculations. The calculated numbers may however not be measurable values. Nevertheless, as orientation data for the interpretation and classification of experimental findings as well as a guideline for new experiments, they form a coordinate system that defines the multidimensional world of chemistry, which corresponds to the Hilbert space formalism of physics. The nonmeasurability of model values is not a weakness of chemistry but a characteristic by which the infinite complexity of the material world becomes scientifically accessible and very useful for chemical research. This review examines the basis of the commonly used quantum chemical methods for calculating molecules and for analyzing their electronic structure. The bonding situation in selected representative molecules of main -group atoms is discussed. The results are compared with textbook knowledge of common chemistry.