In the last decade, there has been a significant development in rapid, non-destructive and non-invasive techniques to evaluate carcass composition and meat quality of meat species. This article aims to review the recent technological advances of non-destructive and non-invasive techniques to provide objective data to evaluate carcass composition and quality traits of sheep and goat meat. We highlight imaging and spectroscopy techniques and practical aspects, such as accuracy, reliability, cost, portability, speed and ease of use. For the imaging techniques, recent improvements in the use of dual-energy X-ray absorptiometry, computed tomography and magnetic resonance imaging to assess sheep and goat carcass and meat quality will be addressed. Optical technologies are gaining importance for monitoring and evaluating the quality and safety of carcasses and meat and, among them, those that deserve more attention are visible and infrared reflectance spectroscopy, hyperspectral imagery and Raman spectroscopy. In this work, advances in research involving these techniques in their application to sheep and goats are presented and discussed. In recent years, there has been substantial investment and research in fast, non-destructive and easy-to-use technology to raise the standards of quality and food safety in all stages of sheep and goat meat production.