I discuss the construction of L-infinity algebras including the special case of the Courant algebroid. Then I elaborate on the general relation between the data of an L-infinity algebra and a classical field theory in theoretical physics. It is argued that there is a one-to-one correspondence between consistent field theories and L-infinity algebras (up to reasonably defined isomorphisms), with the gauge algebra, interactions, etc. of a field theory being encoded in the higher brackets of an L-infinity algebra. I discuss double field theory as a non-trivial example.