Salivary gland dysfunctions are common conditions variously related to aging, inflammatory players, and any other factor able to alter their normal physiology. These conditions may significantly impact oral and systemic health, affecting the overall quality of life. Over time, numerous therapeutic strategies have been explored to regenerate, repair, or replace injured salivary glands, focusing on those molecular and cellular mechanisms able to be safely translated into a clinical landscape. In this context, stem cells, tissue engineering, and the novel organoids technology, have gained exciting results, even if such approaches may require some optimization for their long-term maintenance. Despite extensive research, a composite stem cell population capable of regenerating functional glandular tissue remains elusive; nonetheless, to overcome these current limitations, recently, the transplantation of allogeneic stem cells has emerged as a reliable solution. This overview comprehensively examines the salivary glands in the light of modern biotechnologies, with the aim of better understanding the current state of the art in salivary gland regeneration and repair by using tissue engineering, biomimetic strategies, target therapies, and three-dimensional (3D) organoids technology. This work investigates the main salivary gland dysfunctions and their impact on oral and systemic health. It then discusses the most promising advanced strategies for oral tissue bioengineering, focusing on the potential of stem cells and organoids.