A critical review is given of developments in the theory subsequent to the demonstration that in first approximation 71 --' 37r is forbidden . It remains difficult to understand the process with conventional ideas without reducing to an accident the success of current algebra , and a simple linear matrix element , in K 37T. Quantum Mechanics, High Energy Physics and Accelerators: Selected Papers of John S Bell (With Commentary) Downloaded from www.worldscientific.com by KAINAN UNIVERSITY on 01/05/15. For personal use only. * Our normalizations of currents are those of Bell [3] and Weinberg [ 15]. We take F7T from the pion decay rate. The Goldberger-Treiman formula , F7.=2mNfA( 0)g7TNN gives a value about 12% lower. In the argument of sect . 6 the width r(77 37T) is eventually proportional to Fi4 . An increase of F7, by 12 % corresponds to an increase of r by about 60%. In general authors do not say which value they take for F7,, and this may account for varying answers from similar formulae. Quantum Mechanics, High Energy Physics and Accelerators: Selected Papers of John S Bell (With Commentary) Downloaded from www.worldscientific.com by KAINAN UNIVERSITY on 01/05/15. For personal use only. * See ref . [ 32]. Note especially that in this work the effect of iTl7 mixing is small in comparison with other , rather uncertain , effects arising from ZA and vector meson mixings. ** For discussion and references , see the second paper of ref. [4].