The twenty‐fifth anniversary of the annual Conference on Magnetism and Magnetic Materials offers an appropriate occasion for assessing the significance and physical basis of some unforeseen but important advances in basic magnetism since the middle 1950’s. Three of these advances are (a) the one‐ion (or crystalline field) mechanism of magnetocrystalline anisotropy energy which was synthesized from ingredients investigated in paramagnets and developed into a practical tool for ’’designing’’ ferrimagnets; (b) the recognition of the degeneracy of the spin wave spectrum in ferrimagnetic insulators and its contribution to the establishment of the previously mysterious origins of relaxation in ferrimagnetic resonance; and (c) the concept of magnetic symmetry and its role in ’’legitimizing’’ the previously ’’forbidden’’ (and unobserved) magnetoelectric effect, piezomagnetism, and other phenomena involving considerations of time reversal. Some of these advances occurred gradually rather than abruptly, and none of them appear to have conformed to a pre‐programmed schedule of short‐range goals, milestones, and payoffs. What these advances do have in common is that they were motivated by a need or desire for basic understanding and that they originated in the recognition of a hidden problem or even in unforeseen flashes of physical insight.