We report on the result of some investigations concerning the radiative decays of decuplet baryons and the non-leptonic weak decays of the octet baryons in the context of topological chiral soliton models. Our results are compared with those of alternative baryon models. For the radiative decays we find that the predictions are similar to those of quark models. In the case of the non-leptonic weak decays, we find that although the predicted S-wave amplitudes are in rather good agreement with the observed values, the model s not able to reproduce the empirical P-wave amplitudes. Thus, in contrast to previous expectations, the Skyrme model does not seem to provide a solution to the long-standing “S-wave/P-wave puzzle”.