Nuclear spin systems and magnetic resonance techniques have provided a fertile platform for experimental investigation of quantum state transfer in spin chains. From the first observation of polarization transfer, predating the formal definition of quantum state transfer, to the realization of state transfer simulations in small molecules and in larger solid-state spin systems, the experiments have drawn on the strengths of nuclear magnetic resonance (NMR), in particular on its long history of well-developed control techniques. NMR implementations have been invaluable both as proof-of-principle demonstrations of quantum state transfer protocols and to explore dynamics occurring in real systems that go beyond what can be analytically solved or numerically simulated. In addition, control techniques developed in these systems to engineer the Hamiltonians required for transport can be adopted in potentially scalable quantum information processing architectures. In this contribution we describe recent results and outline future directions of research in magnetic-resonance based implementations of quantum state transfer in spin chains.National Science Foundation (U.S.) (Grant DMR-1005926)United States. Air Force Office of Scientific Research