Optimal control of spin systems.

Quantum optimal control has become a central tool for designing high-performance pulse sequences in magnetic resonance and quantum technologies. Early developments in NMR relied on heuristic composite and shaped pulses or analytical approaches such as average Hamiltonian theory. The introduction of modern optimal control algorithms enabled the systematic optimization of thousands of control parameters, greatly expanding the achievable performance and scope of pulse engineering. This review summarizes key developments in optimal control of spin and pseudo-spin systems and highlights major applications in magnetic resonance, in quantum technologies, and in the control of atoms and molecules.