Biological tissue rheology investigates the mechanical behavior of tissues, emphasizing their viscoelastic and plastic properties that enable both solid-like elasticity and fluid-like viscosity under mechanical stress. These mechanical characteristics are pivotal in various physiological processes, such as embryonic development, tissue remodeling, wound healing, and pathological conditions including cancer metastasis. The mechanical responses of tissues, shaped by cellular forces and extracellular matrix dynamics, are crucial for maintaining tissue integrity and functionality. Rheological behaviors such as viscoelasticity, plasticity, and active mechanical responses underlie critical biological functions, enabling tissues to adapt structurally and functionally to internal and external stimuli. Recent theoretical and experimental advances have illuminated the complex interplay among cellular mechanics, biochemical signaling, and tissue-level forces, highlighting their roles in governing tissue morphogenesis, repair, and disease progression. This review synthesizes current knowledge, identifies key challenges, and discusses future directions for research in biological tissue rheology.