The dictionary between general field theories and strongly homotopy algebras is reviewed and compared with the BV approach, and the use of homotopy transfer to map between theories is discussed. L-infinity algebras are treated both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. An algebraic formulation is provided for the procedure of integrating out of degrees of freedom in field theory in terms of homotopy transfer, giving the induced L-infinity structure of the resulting effective field theory. The construction is illustrated with some examples.