The paper discusses recent advancements in the MFEM (Modular Finite Element Methods) library, a high-performance C++ library for finite element discretizations. Key highlights include: 1. **GPU Acceleration and High-Performance Computing**: MFEM has significantly enhanced its GPU capabilities, supporting GPU-accelerated mesh optimization and solvers for high-order finite element problems. This includes matrix-free solvers, low-order-refined preconditioning, and kernel fusion techniques that improve strong scalability. 2. **Discretization Support**: MFEM now supports a wide range of finite element methods, including discontinuous Petrov-Galerkin (DPG) methods, proximal Galerkin methods, immersed discretizations, and NURBS/IGA. These methods offer advantages such as discrete stability, pointwise bound preservation, and handling implicitly defined geometries. 3. **Meshing Capabilities**: MFEM includes advanced meshing features such as high-order mesh optimization using the Target-Matrix Optimization Paradigm (TMOP), submesh capabilities for multi-domain problems, and support for adaptive mesh refinement. 4. **Applications**: MFEM powers a variety of applications in fields like computational physics, engineering, and machine learning. Examples include random fields and fractional stochastic PDEs, hyperbolic conservation laws, high-order ALE simulations, and electromagnetics applications. 5. **Performance and Portability**: MFEM has been optimized for exascale computing platforms, including AMD GPUs, and has shown good performance portability between NVIDIA and AMD architectures. 6. **Automatic Differentiation**: MFEM integrates with the Enzyme tool to support automatic differentiation, enabling the computation of derivatives in FEM discretizations and optimal design applications. The paper also provides detailed technical descriptions of these advancements, including specific algorithms, implementation details, and performance results.The paper discusses recent advancements in the MFEM (Modular Finite Element Methods) library, a high-performance C++ library for finite element discretizations. Key highlights include: 1. **GPU Acceleration and High-Performance Computing**: MFEM has significantly enhanced its GPU capabilities, supporting GPU-accelerated mesh optimization and solvers for high-order finite element problems. This includes matrix-free solvers, low-order-refined preconditioning, and kernel fusion techniques that improve strong scalability. 2. **Discretization Support**: MFEM now supports a wide range of finite element methods, including discontinuous Petrov-Galerkin (DPG) methods, proximal Galerkin methods, immersed discretizations, and NURBS/IGA. These methods offer advantages such as discrete stability, pointwise bound preservation, and handling implicitly defined geometries. 3. **Meshing Capabilities**: MFEM includes advanced meshing features such as high-order mesh optimization using the Target-Matrix Optimization Paradigm (TMOP), submesh capabilities for multi-domain problems, and support for adaptive mesh refinement. 4. **Applications**: MFEM powers a variety of applications in fields like computational physics, engineering, and machine learning. Examples include random fields and fractional stochastic PDEs, hyperbolic conservation laws, high-order ALE simulations, and electromagnetics applications. 5. **Performance and Portability**: MFEM has been optimized for exascale computing platforms, including AMD GPUs, and has shown good performance portability between NVIDIA and AMD architectures. 6. **Automatic Differentiation**: MFEM integrates with the Enzyme tool to support automatic differentiation, enabling the computation of derivatives in FEM discretizations and optimal design applications. The paper also provides detailed technical descriptions of these advancements, including specific algorithms, implementation details, and performance results.