A review is conducted to discuss the phenomenon of size effect on material strength; the theory of extreme values is the primary analytical tool used. Weibull (1939) was the first to give a reasonably satisfactory explanation of the volume effect on material strength using the “weakest-link” theory. Experimental data showing how strength of cement mortar decreases with volume are compared with the Weibull theory. The agreement is found to be excellent. Fracture in its general setting, regardless of the mechanics of failure, leads to the same problem, namely, the distribution of the smallest value in large samples enabling the use of extreme value theory. A simple derivation reveals that, regardless of the type of extreme value distribution postulated for material strength (Type I, Type II, and Type III), the mean strength shows dependency upon the size. The size effect of fibrous composites obeys the same general relationship as that for brittle materials. Lastly, the weakest-link concept, and thereby size effect, is directly applicable to fatigue strength at an arbitrarily preassigned life N (cycles) but not to the fatigue life. An attempt is made to summarize the present state of knowledge and to identify unsolved problems requiring further research.