The existence of isolated magnetic charges (monopoles) in nature would require profound rethinking not only in elementary particle physics but also in high‐energy cosmic‐ray physics and astrophysics. Monopoles, whose possible existence was first suggested by Dirac in 1931 and whose properties were later recalculated by Schwinger, would be intensely ionizing particles similar in their effects in passing through matter to relativistic rare‐earth ions (or still heavier nuclei). As Parker has noted, only a very minute abundance of monopoles in the galaxy would be necessary to have removed or at least grossly altered the galactic magnetic field on an astrophysically interesting time scale. Solid‐state nuclear track detectors have led to a new series of intensive monopole searches: One of these takes ferromanganese deposits from the deep oceans (as a material which would have magnetically trapped monopoles) and exposes them to high magnetic fields sufficient to loosen monopoles and accelerate them into a detection system; the other experiment is designed to utilize natural detectors (mica and obsidian) to record over geological times the paths of massive, penetrating monopoles. The negative results obtained set new and highly restrictive limits on the abundance of monopoles. These limits are such that the mysterious, high‐energy cosmic rays (1017−1019eV) cannot be monopoles as has been suggested, nor can the galactic magnetic fields be seriously altered by the maximum permitted abundance—even over the galactic age. Finally, the flux of monopoles onto the earth over the earth's entire age is <½ monopole/cm2. Qualifications on these claims are indicated in the article.