We introduce a phase-control holographic technique to characterize scattering media with the purpose of focusing light through it. The system generates computer-generated holograms implemented via a deformable mirror device (DMD) based on micro-electro-mechanical technology. The DMD can be updated at high data rates, enabling high speed wavefront measurements using the transmission matrix method. The transmission matrix of a scattering material determines the hologram required for focusing through the scatterer. We demonstrate this technique measuring a transmission matrix with 256 input modes and a single output mode in 33.8 ms and creating a focus with a signal to background ratio of 160. We also demonstrate focusing through a temporally dynamic, strongly scattering sample with short speckle decorrelation times.