The ability to diagonalise Hamiltonians is a crucial requirement for understanding physical systems. However, for many-particle systems this becomes a complex task, due to the enormous number of degrees of freedom. For a better handling of this difficulty, a variety of different methods have been developed in the last few decades, which allow to make statements about the overall system. One of these methods is based on flow equations, which was proposed by Wegner and Wilson. This approach diagonalises the system Hamiltonian by applying infinitesimal unitary transformations and can be seen as the continuous limit of well-known numerical matrix diagonalisation methods like the QR- or Jacobi-algorithm. However, the method can be reformulated such that the matrix representation is avoided completely and approximations are introduced directly from the operator structure of the Hamiltonian, which makes the flow equation approach a useful tool for gaining numerical and analytical insights into a variety of many-body systems.