AbstractWe present the main ideas behind the statistical bootstrap model and recent developments within this model related to the description of fireball cascade decay.Mathematical methods developed in this model might be useful in other phenomenological schemes of strong interaction physics; they are described in detail.We discuss the present status of applications of the model to various hadronic reactions.When discussing the relations of the statistical bootstrap model to other models of hadron physics we point out possibly fruitful analogies and dynamical mechanisms which are modelled by the bootstrap dynamics under definite conditions. This offers interpretations for the critical temperature typical for the model and indicates further fields of application.