Abstract: Approximate symmetry is a concept that is fundamental for most fields of natural sciences, and it is also an important feature of art. Perfect symmetry is an abstraction of mathematics, seldom, if ever actually realized. Nevertheless, with reference to the ideal, perfect symmetry, it is possible to evaluate, analyse, and appreciate both the scientific relevance and the artistic value of approximate symmetries. Here we shall focus on two such approaches, one based on the concept of symmetry deficiency that also leads to precise measures for the degree of missing symmetry, and on the concept of symmorphy, a generalization of symmetry that also allows for approximate symmetry, yet preserves some of the elegant mathematical tools, such as group theory, which have been found so powerful in utilizing symmetry in chemistry, atomic physics, and even in biology. With these concepts in mind, it is also possible to study and appreciate approximate symmetry in artistic productions.