The Tevatron has inspired new interest in the subject of magnetic monopoles. First there was the 1998 D0 limit on the virtual production of monopoles, based on the theory of Ginzburg and collaborators. In 2000 and 2004 results from an experiment (Fermilab E882) searching for real magnetically charged particles bound to elements from the CDF and D0 detectors were reported. The strongest direct experimental limits, from the CDF collaboration, have been reported in 2005. Less strong, but complementary, limits from the H1 collaboration at HERA were reported in the same year. Interpretation of these experiments also require new developments in theory. Earlier experimental and observational constraints on point-like (Dirac) and non-Abelian monopoles were given from the 1970s through the 1990s, with occasional short-lived positive evidence for such exotic particles reported. The status of the experimental limits on monopole masses will be reported, as well as the limitation of the theory of magnetic charge at present.