ABSTRACT: Constructive and computationally tractable techniques are developed for the classification of complex dynamical systems. These techniques subsume and extend standard dynamical characterizations based on Renyi dimensions and entropy spectra, invariant measures, algorithmic complexities and other dynamical and statistical measures. A natural way of quantifying the complexity of spatio-temporal data sets, and hence the combination of underlying physical system and measuring apparatus, is presented. These methods uniquely associate a data set with a formal language, given a specified model basis. The position of this language in a hierarchy of formal languages provides a measure of the complexity of the data set. This in turn provides a quantitative measure of the experimental or computational resources necessary for the complete characterization of a given system. Examples of data sets produced by various systems and models are analyzed using these techniques. It is shown that these techniques are particularly effective in detecting structure and elucidating underlying mechanisms for complex physical phenomena.