Drop impacts are ubiquitous in nature forming a vital pathway for the transport of liquids, primarily water, and any dissolved substances. The axisymmetric impact of drops has been heavily studied but less work has been done on droplet impacts in which axial symmetry is broken. To analyse such impacts we used a two phase lattice Boltzmann code capable of simulating high density differences. We studied the impact of droplets on cylindrical surfaces, with radius of curvature similar to that of the drop. We found that the symmetry breaking nature of these surfaces leads to droplets bouncing faster and in elongated shapes. The origin of this effect is a positive feedback mechanism through which the momentum asymmetry resulting from the impact grows during retraction. We next looked at how varying the size of the cylinder affected this phenomenon. We found that smaller cylinders increased the contact time reduction, as long as they were still bigger than the droplet, but that below this limit the drop contacted the flat surface and entered a new regime. The work was expanded to look at other types of bouncing asymmetry, using a simple, exactly solvable Lagrangian model. We found that contact time reduction can result from an asymmetric droplet shape, an initially asymmetric velocity or if the surface has an asymmetric drag. A study of the impact of liquid drops containing embedded air bubbles was also undertaken. This was found to lead to jet formation from the bottom of the bubble. We showed how the jet velocity depended on the physical parameters of the drop and impact. In particular the jet formation was very sensitive to the position of the air bubble inside the drop.