The upper limit of strength (the "theoretical strength") has been an active subject of research and speculation for the better part of a century. The subject has recently become important, for two reasons. First, given recent advances in ab initio techniques and computing machines, the limits of strength can be calculated with considerable accuracy, making this one of the very few problems in mechanical behavior that can actually be solved. Second, given recent advances in materials engineering, the limits of strength are being approached in some systems, such as hardened or defect-free films, and their relevance is becoming recognized in others. The present paper discusses some interesting results from recent research on the limits of strength, with an intermixture of speculations based on those results. Topics include the inherent nature of [100 1 cleavage and "pencil slip" in bcc metals, the inherent ductility of fcc metals, the anomalous properties of Al, and the possibility of measuring ideal strength with nanoindentation.