Increasing epidemiological and experimental data now emphasize that a diet rich in vegetables and fruits confers many health benefits. Functional products containing elevated levels of bioactive compounds are attracting considerable attention due to their potential to lower the risk of chronic diseases and their associated huge healthcare costs. On a global scale, there is an increasing demand for berries and fruits, since they are natural polyphenol-rich raw material to be incorporated into functional foods, nutraceuticals and pharmaceuticals. This is a major challenge for both industry and horticultural experts, because the content of health-promoting compounds in plants varies widely not only in different plant species, but also between cultivars. The content is also significantly affected by harvesting, storage and processing factors. This review summarizes the recent data and clarifies the main contributors of harvesting time, various storage conditions and post-harvest procedures, such as temperature management, controlled atmosphere, 1-MCP, calcium and plant activators, as ways to influence health-promoting compounds in fruits. Furthermore, the ways processing factors, e.g., enzymatic treatment, pressing, clarification, temperature, pressure and fermentation, can influence the levels of polyphenols and vitamins in berries and soft fruits will be discussed. Finally, strategies for preventing the decline of health-promoting compounds in fruits during long-term storage will be assessed in light of recent scientific progress and modern methods, which preserve the levels of polyphenols, will be highlighted.