Atoms, the smallest divisions of matter that retain the chemical properties of bulk matter, have long been understood to possess internal structure -- of the electrons bound to the nuclei by Coulomb forces.  The spectroscopic evidence for discrete energy states of internal motion led, long ago, to theoretical descriptions by Lorentz, by Bohr and Rutherford, and by Hartree. Given such stationary structures, the tools of laser light pulses allow an experimenter to alter the internal motion -- to produce specific internal structures of atoms and molecules. The theoretical description of such atomic dynamics has altered over the last 3 decades, from the rate equations firstproposed by Einstein to the contemporary use of the time-dependent Schroedinger equation, exemplified by sets of coupled linear first order differential equations. Solutions of these equations, appropriate to laser pulse-induced excitation of specific quantum states of atoms or molecules, continue to provide a wealth of novel processes whose uses are very much in the forefront of contemporaryresearch in fundamental and applied physics. I will provide an introduction and overview of this physics, with examples of "counter-intuitive" behavior.