This talk presents a reliable and efficient residual-based a posteriori error analysis for the symmetric H(divdiv) mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary conditions. The key ingredient lies in the construction of boundary condition-preserving complexes at both continuous and discrete levels. Furthermore, the discrete symmetric H(divdiv) space is extended to ensure nestedness, which leads to optimality for the adaptive algorithm. Some numerical examples are provided to show the effectiveness of the a posteriori error estimator.