In this thesis, a systematic study was performed to understand drop impact onto hydrophilic and hydrophobic moving surfaces. Different systems (combination of liquids, surfaces, and drop impact conditions) were examined. Wide range of normal drop and surface velocities were studied; such normal and tangential velocity ranges are not available in systems where a drop impacts at an angle relative to a surface. The asymmetric nature of drop spreading on moving surfaces was elucidated. A model that for the first time is able to mathematically predict the time evolution of such asymmetric spreading was provided. Furthermore, a new model was developed to determine the splashing threshold of the drop impact onto a moving surface. The model is capable of describing the azimuthally different behavior of splashing. The effect of liquid viscosity on drop splashing was clarified. A comprehensive regime maps of drop impact outcome on a moving surface was provided