Advances in the subject of plasma containment in cusp-shaped magnetic fields over the past six or more years are reviewed. Particular emphasis is placed on the structure and thickness of the sheath separating a field-free plasma from a vacuum magnetic field. Recent experimental results suggest possibly that the thickness could be the geometric mean of the electron and ion Larmor radii, compared to earlier results in which the thickness measured was nearer the ion Larmor radius. The electric field in the sheath is important not only in determining its structure but also in problems associated with flow, end shorting, losses, and plasma rotation and stability. The present status of radio-frequency and electrostatic plugging of the ends is presented. Liner implosion to obtain extreme, and perhaps optimal, conditions for controlled fusion is a new aspect of this subject which deserves some attention. Hybrid schemes which employ cuspshaped magnetic fields as an essential part of their containment configuration include the linear picket fence, the spherical multipole magnetic trap, the stuffed cusp, the caulked stuffed cusp, the caulked cusp torus (CCT), the toroidal line cusp (or Tormac), and the containment of a flowing plasma in toroidal multiple cusps (the Polytron). These are reviewed, and their advantages and disadvantages for fusion are discussed.