Light scattering in inhomogeneous media induces wavefront distortions that pose an inherent limitation in many optical applications. Examples where this occurs include microscopy, nanosurgery and astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible using wavefront-shaping techniques. However, when ultrashort pulses are used, scattering also induces temporal distortions, which hinder the use of such pulses in nonlinear processes such as multiphoton microscopy and quantum control experiments. Here, we show that correction of both spatial and temporal distortions can be achieved by manipulating only the spatial degrees of freedom of the incident wavefront. By optimizing a nonlinear signal, we demonstrate spatiotemporal focusing and compression of chirped ultrashort pulses through scattering media, and refocusing in both space and time of 100 fs pulses through thick brain and bone samples. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media.