The possibility of controlled direct laser-nuclear excitations is considered from a quantum control perspective. The controllability of laser-driven electric dipole and magnetic dipole transitions among pure nuclear states is analyzed. Within a set of realistic and general conditions, atomic nuclei are demonstrated to possess full state controllability. Additionally, an analysis of the nuclear state excitation probability as a function of the laser control field is conducted. This control landscape is shown to possess a generic topology, which has important physical consequences for achieving optimal nuclear state excitation with laser fields. Last, an assessment is given of the technological challenges that need to be considered when implementing direct nuclear control in the laboratory.