Traditional metal-organic-frameworks (MOFs) have been extensively studied and applied in various fields across chemistry, biology and engineering in the past decades. Recently, a family of emerging MOF liquids and glasses have gained ever-growing research interests owing to their fascinating phase transitions and unique functions. To date, a growing number of MOF crystals have been found to be capable of transforming into liquid and glassy states under external stimuli, which overcomes the limitations of MOF crystals by introducing functional disorder in a controlled manner and offering some desirable properties. This review is dedicated to compiling recent advances in the fundamental understanding of the phase and structure evolution during crystal melting and glass formation in order to give insights into the underlying conversion mechanism. Benefiting from the disordered metal-ligand arrangement and free grain boundaries, various functional properties of liquid and glassy MOFs including porosity, ionic conductivity, and optical/mechanical properties are summarized and evaluated in detail, accompanied by the structure-property correlation. At the same time, their potential applications are further assessed from a developmental perspective according to their unique functions. Finally, we summarize the current progress in the development of liquid/glassy MOFs and point out the serious challenges as well as the potential solutions. This work provides perspectives on the functional applications of liquid/glassy MOFs and highlights the future research directions for the advancement of MOF liquids and glasses.