Aircraft wing droop leading edge apparatus and methods are described. An example aircraft includes a wing having a front spar and an outer skin covering the front spar. The outer skin includes a forward portion located forward of the front spar. The forward portion of the outer skin includes a leading edge movable between a neutral position and a drooped position deflected downward relative to the neutral position. The forward portion of the outer skin has a continuous outer mold line when the leading edge is in the drooped position.