One of the most successful time-dependent quantum many-body theories is time-dependent density functional theory (TDDFT) which has been applied to atoms, molecules, nuclei and solids especially whenever the number of degrees of freedom prevents the application of more sophisticated methods. TDDFT, however, suffers from fundamental difficulties: apart from the theoretical statement that the density contains all information about the full wavefunction there is no known method for how to exactly incorporate exchange and correlation effects during time propagation and how information beyond spatial one-particle observables can be extracted. We have recently developed a new theory based on the two-particle reduced density matrix which overcomes some of these difficulties since both the energy functional and the equations of motion are known exactly. We give an overview of this theory, discuss its limitations, and demonstrate its application to electronic strong field dynamics in small molecules.