This paper critically examines the various direct and indirect methods for determining the tensile strength of concrete. The direct methods considered are the classical uniaxial tension tests, the modified direct tension test due to Todd, and the very recent methods in which thick steel plates are glued by means of epoxies to the ends of concrete specimens, which are then broken in tension. The inherent problems of parasitic stresses due to clamping and misalignment in these tests are outlined and discussed. The indirect methods examined vary from bending tests, first proposed around 1904, to the cylinder and cube splitting tension tests, advanced in 1940 and 1960 respectively, and the ring tensile test proposed in 1965. The errors introduced in these tests due to the assumptions based upon the Hooke's Law of linear Stress-strain Proportionality are outlined, and an attempt has been made to correct the strength values obtained in these tests to derive the "true" tensile strength of the concrete. The reproducibility of the strength-test results for the various methods is given, and relationships have been attempted between the different types of strength. The advantages and disadvantages of both direct and indirect tension test methods are given. The most common methods are illustrated by photographs or line drawings and over 100 pertinent references are listed.