The notion of a double Lie algebroid was introduced by Kirill Mackenzie in a 1992 paper, as a double vector bundle D equipped with two Lie algebroid structures satisfying certain compatibility conditions. A main example is the tangent bundle of a Lie algebroid. In 2012, Ted Voronov proved that double Lie algebroid structures may be described as a pair of commuting homological vector fields on the supermanifold D[1, 1]. This talk is a ‘classical’ description of this theory, with special attention to duality operations. (Based on joint work with Jeff Pike.)