The field of numerical methods for nonlinear diffusion and poroelasticity is rapidly advancing, with a focus on developing efficient and accurate algorithms for solving complex problems. Recent developments have centered around the creation of new finite element methods, such as the active flux method and the virtual element method, which offer improved accuracy and stability for solving nonlinear diffusion equations. Additionally, there has been significant progress in the development of multiscale methods, such as the multiscale graph reduction algorithm, which enable the efficient simulation of heterogeneous and anisotropic diffusion processes. The use of novel numerical techniques, such as the parareal algorithm and the spectral Galerkin discretization, has also been explored for solving quasilinear subdiffusion equations. Noteworthy papers in this area include the development of a fourth-order active flux method for parabolic problems, which demonstrates high accuracy and efficiency for solving the porous medium equation, and the proposal of a fully mixed virtual element scheme for steady-state poroelastic stress-assisted diffusion, which offers a robust and efficient method for solving coupled problems in poromechanics.