The field of numerical methods for complex fluids and contact problems is rapidly advancing, with a focus on developing innovative and efficient algorithms for simulating real-world phenomena. Recent research has centered on creating stable, high-order, and structure-preserving schemes for various fluid models, including the Oldroyd-B and Carreau fluid equations. These schemes aim to accurately capture the behavior of viscoelastic fluids and ionic transport, while also preserving key physical properties such as positivity and energy stability. Additionally, there has been significant progress in the development of virtual element methods and stabilization techniques for solving contact problems, including the third medium contact approach. These methods have shown promise in handling complex geometries and large deformations, and have been successfully applied to a range of engineering applications. Noteworthy papers in this area include: A paper presenting a linear, decoupled, positivity preserving scheme for the diffusive Oldroyd-B coupled with PNP model, which demonstrates the ability to handle high Weissenberg numbers and accurately capture the flow structure influenced by elastic effects. A paper introducing a novel stabilization strategy for high-order incompressible flow solvers, which achieves high accuracy and convergence while ensuring compatibility with high-order elements on unstructured meshes. A paper proposing a new contact algorithm based on the Fiber Monte Carlo method, which accurately computes contact forces for complex geometries and eliminates the need for master-slave identification and projection iterations.