This paper presents an overview of multisource inverse-geometry computed tomography (IGCT) as well as the development of a gantry-based research prototype system. The development of the distributed x-ray source is covered in a companion paper [V. B. Neculaes et al., "Multisource inverse-geometry CT. Part II. X-ray source design and prototype," Med. Phys. 43, 4617-4627 (2016)]. While progress updates of this development have been presented at conferences and in journal papers, this paper is the first comprehensive overview of the multisource inverse-geometry CT concept and prototype. The authors also provide a review of all previous IGCT related publications. The authors designed and implemented a gantry-based 32-source IGCT scanner with 22 cm field-of-view, 16 cm z-coverage, 1 s rotation time, 1.09 × 1.024 mm detector cell size, as low as 0.4 × 0.8 mm focal spot size and 80-140 kVp x-ray source voltage. The system is built using commercially available CT components and a custom made distributed x-ray source. The authors developed dedicated controls, calibrations, and reconstruction algorithms and evaluated the system performance using phantoms and small animals. The authors performed IGCT system experiments and demonstrated tube current up to 125 mA with up to 32 focal spots. The authors measured a spatial resolution of 13 lp/cm at 5% cutoff. The scatter-to-primary ratio is estimated 62% for a 32 cm water phantom at 140 kVp. The authors scanned several phantoms and small animals. The initial images have relatively high noise due to the low x-ray flux levels but minimal artifacts. IGCT has unique benefits in terms of dose-efficiency and cone-beam artifacts, but comes with challenges in terms of scattered radiation and x-ray flux limits. To the authors' knowledge, their prototype is the first gantry-based IGCT scanner. The authors summarized the design and implementation of the scanner and the authors presented results with phantoms and small animals.