Methods for deep-penetration radiation transport remain important for radiation shielding, nonproliferation, nuclear threat reduction, and medical applications. As these applications become more ubiquitous, the need for accurate and reliable transport methods appropriate for these systems persists. For such systems, hybrid methods often obtain reliable answers in the shortest time by leveraging the speed and uniform uncertainty distribution of a deterministic solution to bias Monte Carlo transport and reduce the variance in the solution. This work reviews the state of the art among such hybrid methods. First, we summarize variance reduction (VR) for Monte Carlo radiation transport and existing efforts to automate these techniques. Relations among VR, importance, and the adjoint solution of the neutron transport equation are then discussed. Based on this exposition, the work transitions from theory to a critical review of existing VR implementations in modern nuclear engineering software. At present, the Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS) hybrid methods are the gold standard by which to reduce the variance in problems that have deeply penetrating radiation. The CADIS and FW-CADIS methods use an adjoint scalar flux to generate VR parameters for Monte Carlo radiation transport. Additionally, efforts to incorporate angular information into VR methods for Monte Carlo are summarized. Finally, we assess various implementations of these methods and the degree to which they improve VR for their target applications.