In this talk, we will construct the dark and breather solutions to the Fokas-Lenells (FL)equation by the KP reduction method. The FL equation gives a set of three bilinear equations. However, one of these bilinear equations cannot be obtained directly from the bilinear equations of the KP-Toda hierarchy. Instead, we have to introduce an auxiliary tau fucntion and start from four bilinear equations to reduce to this particular bilinear equations. The rogue wave solution can be constructed in a similar way.