I will review results obtained in collaboration with Pavel Winternitz on the structure and classification of Lie algebras and published in a joint monograph. Next, I will illustrate their usefulness on an example of mathematically equivalent equations describing physically different situations in fluid dynamics. I will also show that Lie algebras can be encountered in the theory of superintegrable systems, i.e. Hamiltonian systems possessing more integrals of motion than needed for integrability in Liouville sense.