Goats and sheep are valuable as they are a source of meat, milk, fleece, and other products. These livestock are also important both for agriculture and biomedical research. However, the efficient, sustainable, and profitable production of these small ruminants faces major obstacles. Hence, this review analyzes these major challenges specifically, their negative impacts on the industry, and suggests some science-based solutions to overcome them. Those challenged areas are education and training, research, translational research/biotechnology, goat and sheep health, and maintenance of an economically sustainable agribusiness. The suggested solutions include the effective teaching of goat and sheep science to the next generation and public empowerment, support for innovative and translational research, disease prevention and treatment, support for technology transfer, and development of sound agribusiness practices. This review is helpful particularly for scientists, students, and the goat and sheep producers. In general, these information on the current state of goat and sheep agriculture will also help the public to better understand and appreciate the challenges met and opportunities provided in small ruminant production enterprises.