The field of neural networks is witnessing significant developments with the Neural Tangent Kernel (NTK) at its forefront. Recent research has focused on improving the efficiency and effectiveness of NTK-based methods, enabling faster analysis and applications. A key direction is the development of matrix-free approaches, which can yield speedups of many orders of magnitude. Another area of innovation is the use of NTK-guided methods for accelerating training and improving representation quality. Noteworthy papers include: NTK-Guided Implicit Neural Teaching, which proposes a novel approach for accelerating training by dynamically selecting coordinates that maximize global functional updates. Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Loss, which proves the convergence of an adaptive weighting algorithm and develops a randomized algorithm for efficient computation of NTK-based weights.