The invisibility cloak as a longstanding fantastic dream for humans is now within the realm of possibility, thanks to the development of metamaterials. Transformation-optics-based invisibility cloaks have been proposed and realized in many frequency ranges by utilizing gradient-index metamaterials. However, due to the large size of device and difficulty in fabrication, transformation-optics-based invisibility cloaks are significantly limited in practical applications. Recently, metasurfaces as the 2D counterpart of metamaterials have attracted tremendous interests because of its thin thickness and strong capability in manipulating the electromagnetic waves. Ultrathin invisibility cloaks based on metasurfaces release the demand on bulky sizes and extreme parameters, thus promoting further development of invisibility cloaks. This review overviewed recent progress in ultrathin invisibility cloaks based on metasurfaces, focusing particularly on the working principles, implementation methods, advantages and disadvantages. Finally, some advice was put forward on the trends of this fast-developing research field.