Bifidobacterium species are essential members of a healthy human gut microbiota. Their presence in the gut is associated with numerous health outcomes such as protection against gastrointestinal tract infections, inflammation, and metabolic diseases. Regular intake of Bifidobacterium in foods is a sustainable way of maintaining the health benefits associated with its use as a probiotic. Owing to their global acceptance, fermented dairy products (particularly yogurt) are considered the ideal probiotic carrier foods. As envisioned in the definition of probiotics as “live organisms,” the therapeutic functionalities of Bifidobacterium spp. depend on maintaining their viability in the foods up to the point of consumption. However, sustaining Bifidobacterium spp. viability during the manufacture and shelf-life of fermented dairy products remains challenging. Hence, this paper discusses the significance of viability as a prerequisite for Bifidobacterium spp. probiotic functionality. The paper focuses on the stress factors that influence Bifidobacterium spp. viability during the manufacture and shelf life of yogurt as an archetypical fermented dairy product that is widely accepted as a delivery vehicle for probiotics. It further expounds the Bifidobacterium spp. physiological and genetic stress response mechanisms as well as the methods for viability retention in yogurt, such as microencapsulation, use of oxygen scavenging lactic acid bacterial strains, and stress-protective agents. The report also explores the topic of viability determination as a critical factor in probiotic quality assurance, wherein, the limitations of culture-based enumeration methods, the challenges of species and strain resolution in the presence of lactic acid bacterial starter and probiotic species are discussed. Finally, new developments and potential applications of next-generation viability determination methods such as flow cytometry, propidium monoazide–quantitative polymerase chain reaction (PMA-qPCR), next-generation sequencing, and single-cell Raman spectroscopy (SCRS) methods are examined.