The Miniball germanium detector array has been operational at the REX (Radioactive ion beam EXperiment) post accelerator at the Isotope Separator On-Line facility ISOLDE at CERN since 2001. During the last decade, a series of successful Coulomb excitation and transfer reaction studies have been performed with this array, utilizing the unique and high-quality radioactive ion beams which are available at ISOLDE. In this article, an overview is given of the technical details of the full Miniball setup, including a description of the γ-ray and particle detectors, beam monitoring devices and methods to deal with beam contamination. The specific timing properties of the REX-ISOLDE facility are highlighted to indicate the sensitivity that can be achieved with the full Miniball setup. The article is finalized with a summary of some physics highlights at REX-ISOLDE and the utilization of the Miniball germanium detectors at other facilities.