A key challenge in standard Finite Element Methods is the requirement for mesh conformity. This constraint often forces the refinement of elements that do not significantly contribute to the global error estimator, driven essentially by geometric considerations. The Virtual Element Method (VEM) offers a novel perspective to overcome this limitation. VEM permits the use of elements with hanging nodes, treating them as aligned edges or faces, thereby relaxing the mesh conformity requirement and improving flexibility. This talk will go through the adaptive theory of VEM, initiated in [1], with particular emphasis on higher-order methods [2] and the three-dimensional case [3]. We introduce new stabilization-free a posteriori error estimates and propose an adaptive algorithm, proving its convergence. REFERENCES [1] L. Beirao da Veiga, C. Canuto, R. H. Nochetto, G. Vacca, G. and M. Verani, Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property. SIAM J. Numer. Anal., Vol. 61 (2), pp. 457–494, 2023. [2] C. Canuto and D. Fassino, Higher-order adaptive virtual element methods with contraction properties. Math. Eng., Vol. 5 (6), pp. 1–33, 2023. [3] S. Berrone, D. Fassino and F. Vicini, 3D Adaptive VEM with stabilization-free a posteriori error bounds. Submitted for publication, 2024.