Context. Computational astrophysics nowadays routinely combines grid-adaptive capabilities with modern shock-capturing, high resolution spatio-temporal integration schemes in challenging multidimensional hydrodynamic and magnetohydrodynamic (MHD) simulations. A large, and still growing, body of community software exists, and we provide an update on recent developments within the open-source MPI-AMRVAC code. Aims. Complete with online documentation, the MPI-AMRVAC 3.0 release includes several recently added equation sets and offers many options to explore and quantify the influence of implementation details. While showcasing this flexibility on a variety of hydro-dynamic and MHD tests, we document new modules of direct interest for state-of-the-art solar applications. Methods. Test cases address how higher-order reconstruction strategies impact long-term simulations of shear layers, with and without gas-dust coupling effects, how runaway radiative losses can transit to intricate multi-temperature, multiphase dynamics, and how different flavors of spatio-temporal schemes and/or magnetic monopole control produce overall consistent MHD results in combination with adaptive meshes. We demonstrate the use of super-time-stepping strategies for specific parabolic terms and give details on all the implemented implicit-explicit integrators. A new magneto-frictional module can be used to compute force-free magnetic field configurations or for data-driven time-dependent evolutions, while the regularized-Biot-Savart-law approach can insert flux ropes in 3D domains. Synthetic observations of 3D MHD simulations can now be rendered on the fly, or in post-processing, in many spectral wavebands. Results. A particle module as well as a generic field line tracing module, fully compatible with the hierarchical meshes, can be used to do anything from sampling information at prescribed locations, to following the dynamics of charged particles and realizing fully two-way coupled simulations between MHD setups and field-aligned nonthermal processes. We provide reproducible, fully demonstrated tests of all code functionalities. Conclusions. While highlighting the latest additions and various technical aspects (e.g., reading in datacubes for initial or boundary conditions), our open-source strategy welcomes any further code usage, contribution, or spin-off development.