Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization or when using high-order fully implicit numerical methods for time solution of semi-discretized PDEs. This mini-symposium will delve into the evolving field of preconditioning, bringing together researchers who are currently developing efficient preconditioning approaches for a variety of scientific applications. Topics of interest include algebraic preconditioners, Multigrid, and Schur complement-based preconditioners for multiple saddle point linear systems that emerge from multiphysics problems. Additionally, advancements in data-driven methods, including recent operator learning approaches, will be discussed. Spectral and or field of values analysis of the preconditioned matrices, inexact solvers, GPU parallel implementation, and efficiency and scalability aspects on High-performance computing systems will also be covered. Randomized algorithms and the investigation of Mixed-precision for preconditioning are also of significant interest.