With recent advances in wavefront shaping techniques for imaging and telecommunications, the question of a theoretical description of coherently controlled waves in complex media has become increasingly important. Indeed, these waves elude incoherent propagation theories such as radiative transport theory. Moreover, macroscopic approaches such as random matrix theory lack the flexibility to incorporate realistic experimental conditions such as quasiballistic effects, complex geometries, absorption, or incomplete wave control. In this work, I introduce a general theoretical framework for shaped waves valid under these conditions. At the heart of this theory lies a transport equation similar to the radiative transport equation but for a matrix function. This equation captures not only the statistical distribution of transmission eigenvalues in random media, but also the intensity profile of transmission eigenstates, whose sinusoidal shape remained unexplained for a decade.