While the original paper about Yagi-Uda antennas was focused (no pun intended) on VHF and UHF applications, there is nothing about that range that is specific to the Yagi design. On the low frequency side, the limits are the physical size of the structure. On the high frequency side, manufacturing tolerances, plus the effectiveness of other of Yagis.
At upper HF and into the UHF range, Yagis tend to be made from rigid, self-supporting materials, such as aluminum tubing. At the low end, they are more often found as fixed antennas constructed of wire elements. At the upper end of the frequency range, they are sometimes even seen etched onto printed circuit material.