This chapter focuses on several theoretical and experimental studies of the response of matter to light with an emphasis on semiconductors and fast-intense laser pulses. This method is called tight-binding electronion dynamics (TED), because it permits simulations of the coupled dynamics of valence electrons and ion cores in a molecule or material and it employs a tight-binding representation for the electronic states. It is applicable to general non-adiabatic processes including interactions with an intense radiation field. TED is a technique for simulating the coupled dynamics of valence electrons and ion cores in a molecule or material. One of the great strengths of TED is that the structural response is treated at the same time as the electronic response. TED is a promising approach for biological molecules and complex materials because it is inherently an O(N) method. The chapter presents the results for various interesting phenomena involving the response of H2 + to fast-intense laser pulses for the absorption and dichroism of chlorophyll and for a conformational change in butadiene.