Tactile sensing plays a pivotal role in achieving precise physical manipulation tasks and extracting vital physical features. This comprehensive review paper presents an in-depth overview of the growing research on tactile-sensing technologies, encompassing state-of-the-art techniques, future prospects, and current limitations. The paper focuses on tactile hardware, algorithmic complexities, and the distinct features offered by each sensor. This paper has a special emphasis on agri-food manipulation and relevant tactile-sensing technologies. It highlights key areas in agri-food manipulation, including robotic harvesting, food item manipulation, and feature evaluation, such as fruit ripeness assessment, along with the emerging field of kitchen robotics. Through this interdisciplinary exploration, we aim to inspire researchers, engineers, and practitioners to harness the power of tactile-sensing technology for transformative advancements in agri-food robotics. By providing a comprehensive understanding of the current landscape and future prospects, this review paper serves as a valuable resource for driving progress in the field of tactile sensing and its application in agri-food systems.