In this paper we give a comprehensive presentation of the disconnection tableau calculus, a proof method for formulas in classical first-order clause logic. The distinguishing property of this calculus is that it uses unification in such a manner that important proof-theoretic advantages of the classical (i.e., Smullyan-style) tableau calculus are preserved, specifically the termination and model generation characteristics for certain formula classes. Additionally, the calculus is well suited for fully automated proof search. The calculus is described in detail with soundness and completeness proofs, and a number of important calculus refinements developed over the past years are presented. Referring to the model-finding abilities of the disconnection calculus, we explain the extraction and representation of models. We also describe the integration of paramodulation-based equality handling. Finally, we give an overview of related methods.