High current pulsed-power generators efficiently store and deliver magnetic energy to z-pinch targets. We review applications of magnetically driven implosions (MDIs) to inertial confinement fusion. Previous research on MDIs of wire-array z-pinches for radiation-driven indirect-drive target designs is summarized. Indirect-drive designs are compared with new targets that are imploded by direct application of magnetic pressure produced by the pulsed-power current pulse. We describe target design elements such as larger absorbed energy, magnetized and pre-heated fuel, and cryogenic fuel layers that may relax fusion requirements. These elements are embodied in the magnetized liner inertial fusion (MagLIF) concept [Slutz “Pulsed-power-driven cylindrical liner implosions of laser pre-heated fuel magnetized with an axial field,” Phys. Plasmas, 17, 056303 (2010), and Stephen A. Slutz and Roger A. Vesey, “High-Gain Magnetized Inertial Fusion,” Phys. Rev. Lett., 108, 025003 (2012)]. MagLIF is in the class of magneto-inertial fusion targets. In MagLIF, the large drive currents produce an azimuthal magnetic field that compresses cylindrical liners containing pre-heated and axially pre-magnetized fusion fuel. Scientific breakeven may be achievable on the Z facility with this concept. Simulations of MagLIF with deuterium-tritium fuel indicate that the fusion energy yield can exceed the energy invested in heating the fuel at a peak drive current of about 27 MA. Scientific breakeven does not require alpha particle self-heating and is therefore not equivalent to ignition. Capabilities to perform these experiments will be developed on Z starting in 2013. These simulations and predictions must be validated against a series of experiments over the next five years. Near-term experiments are planned at drive currents of 16 MA with D2 fuel. MagLIF increases the efficiency of coupling energy (=target absorbed energy/driver stored energy) to targe- s by 10-150X relative to indirect-drive targets. MagLIF also increases the absolute energy absorbed by the target by 10-50X relative to indirect-drive targets. These increases could lead to higher fusion gains and yields. Single-shot high yields are of great utility to national security missions. Higher efficiency and higher gains may also translate into more compelling (lower cost and complexity) fusion reactor designs. We will discuss the broad goals of the emerging research on the MagLIF concept and identify some of the challenges. We will also summarize advances in pulsed-power technology and pulsed-power driver architectures that double the efficiency of the driver.