Epithelia are robust tissues that support the structure of embryos and organs and serve as effective barriers against pathogens. Epithelia also chemically separate different physiological environments. These vital functions require tight association between cells through the assembly of junctions that mechanically stabilize the tissue. Remarkably, epithelia are also dynamic and can display a fluid behavior. Cells continuously die or divide, thereby allowing functional tissue homeostasis. Epithelial cells can change shape or intercalate as tissues deform during morphogenesis. We review the mechanical basis of tissue robustness and fluidity, with an emphasis on the pivotal role of junction dynamics. Tissue fluidity emerges from local active stresses acting at cell interfaces and allows the maintenance of epithelial organization during morphogenesis and tissue renewal.