In yeast, aging is widely understood as the decline of physiological function and the decreasing ability to adapt to environmental changes. Saccharomyces cerevisiae has become an important model organism for the investigation of these processes. Yeast is used in industrial processes (beer and wine production), and several stress conditions can influence its intracellular aging processes. The aim of this review is to summarize the current knowledge on applied stress conditions, such as osmotic pressure, primary metabolites (e.g., ethanol), low pH, oxidative stress, heat on aging indicators, age-related physiological changes, and yeast longevity. There is clear evidence that yeast cells are exposed to many stressors influencing viability and vitality, leading to an age-related shift in age distribution. Currently, there is a lack of rapid, non-invasive methods allowing the investigation of aspects of yeast aging in real time on a single-cell basis using the high-throughput approach. Methods such as micromanipulation, centrifugal elutriator, or biotinylation do not provide real-time information on age distributions in industrial processes. In contrast, innovative approaches, such as non-invasive fluorescence coupled flow cytometry intended for high-throughput measurements, could be promising for determining the replicative age of yeast cells in fermentation and its impact on industrial stress conditions.