Non-bovine dairy animals, commonly referred to as non-traditional dairy species, include goats, sheep, yaks, buffalo, donkeys, alpacas, llamas, and other less commonly farmed species. These animals have been integral to livestock systems since ancient times, providing milk and other essential products. Despite their historical significance, dairy production from many of these species remains predominantly confined to rural areas in developing countries, where scientific advancements and technical improvements are often limited. As a consequence of this, the scientific literature and technological developments in the processing and characterization of dairy products from these species have lagged behind those for cow’s milk. This review aims to compile and analyze existing research on dairy products derived from non-traditional animals, focusing on their molecular characteristics, including proteins (alpha, beta, kappa, and total casein), fats (cholesterol and total fat), lactose, albumin, ash, total solids, and somatic cell count, among others, for each of these species. Additionally, we discuss emerging technologies employed in their processing, encompassing both non-thermal methods (such as high-pressure processing, pulsed electric fields, ultrasound processing, UV-C irradiation, gamma radiation, microfiltration, and cold plasma processing) and thermal methods (such as ohmic heating). This review also explores the specific potential applications and challenges of implementing these technologies. By synthesizing recent findings, we aim to stimulate further research into innovative technologies and strategies that can enhance the quality and yield of non-bovine dairy products. Understanding the unique properties of milk from these species may lead to new opportunities for product development, improved processing methods, and increased commercialization in both developing and developed markets.