The field of vector search and indexing is witnessing significant advancements, driven by the need for efficient and scalable solutions. Researchers are exploring innovative methods to improve the performance of vector search algorithms, including the use of adaptive awareness capabilities, geometric transformations, and machine learning models. These approaches aim to address the challenges of high-dimensional data, such as local optima and redundant computations, and provide more accurate and efficient search results. Notable papers in this area include: Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products, which presents a new codebook representation that supports efficient clean-up with linearithmic time complexity. Empowering Graph-based Approximate Nearest Neighbor Search with Adaptive Awareness Capabilities, which proposes a lightweight and adaptive module to accelerate approximate nearest neighbor search. Filter-Centric Vector Indexing: Geometric Transformation for Efficient Filtered Vector Search, which introduces a novel framework that transforms the fundamental trade-off between performance and accuracy in vector search. The kernel of graph indices for vector search, which leverages kernel methods to establish graph connectivity and provides formal navigability guarantees valid in metric and non-metric vector spaces.