This talk presents recent advances in scalable implicit solvers for continuum kinetic runaway electron modeling, focusing on two complementary developments: dynamic adaptive mesh refinement (AMR) and robust algebraic multigrid (AMG) preconditioning for large-scale parallel simulations. We develop a new adaptive solver based on PETSc and p4est that integrates dynamic AMR, distributed-memory parallelism, and fully implicit time integration. To efficiently solve the linear systems arising from implicit discretizations, we further develop a reduction-based AMG preconditioner based on local approximate ideal restriction. Numerical results demonstrate robust convergence across a wide range of electric-field strengths, near mesh-independent iteration counts on adaptive meshes, and strong parallel scalability, enabling scalable, high-fidelity runaway electron simulations.