  We review and develop the general properties of $L_\infty$ algebras focusing
on the gauge structure of the associated field theories. Motivated by the
$L_\infty$ homotopy Lie algebra of closed string field theory and the work of
Roytenberg and Weinstein describing the Courant bracket in this language we
investigate the $L_\infty$ structure of general gauge invariant perturbative
field theories. We sketch such formulations for non-abelian gauge theories,
Einstein gravity, and for double field theory. We find that there is an
$L_\infty$ algebra for the gauge structure and a larger one for the full
interacting field theory. Theories where the gauge structure is a strict Lie
algebra often require the full $L_\infty$ algebra for the interacting theory.
The analysis suggests that $L_\infty$ algebras provide a classification of
perturbative gauge invariant classical field theories.
