Isogeometric Analysis has been proven to be a suitable tool for the discretization of higher-order formulations describing phenomena like brittle fracture or phase separation in fluid mixtures [1,2]. In this context, phase-field models constitute a convenient approach to model sharp interface problems, since they incorporate a continuous field variable --the field order parameter-- to describe the transition between the phases, allowing for an automatic tracking of the evolution of the smooth interfaces. From a computational standpoint, phase-field models need fine meshes, at least locally, in order to accurately resolve the phase-field profile. This factor becomes particularly critical in volumetric domains, where the computational cost is a major concern. We present a higher-order adaptive isogeometric framework for volumetric phase-field problems, exemplified by the Cahn--Hilliard equation. Truncated Hierarchical B-splines (THB-splines) provide a flexible basis supporting local refinement and coarsening [3,4], enabling efficient resolution of evolving interfaces in 2D and 3D. Our adaptive scheme automatically refines the mesh at phase interfaces and coarsens it in the bulk, with solution transfer between successive meshes handled via a quasi-interpolation operator that is parallelizable and computationally efficient. We demonstrate the effectiveness of this approach through numerical studies that highlight the method’s ability to accurately track interfaces, illustrating the advantages of mesh adaptivity in complex volumetric phase-field simulations. [1] Greco, L., Patton, A., Negri, M., Marengo, A., Perego, U., and Reali, A. (2024). Higher order phase-field modeling of brittle fracture via isogeometric analysis. Engineering with Computers, 40, 3541–3560. [2] Gómez, H., Calo, V. M., Bazilevs, Y., and Hughes, T. J. (2008). Isogeometric analysis of the Cahn–Hilliard phase-field model. Computer Methods in Applied Mechanics and Engineering, 197(49-50), 4333-4352. [3] Giannelli, C., Jüttler, B., and Speleers, H. (2012). THB-splines: The truncated basis for hierarchical splines. Computer Aided Geometric Design, 29(7), 485-498. [4] Carraturo, M., Giannelli, C., Reali, A., and Vázquez, R. (2019). Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes. Computer Methods in Applied Mechanics and Engineering, 348, 660-679.