Magnetic fields pervade astrophysical systems and strongly influence their dynamics. Because magnetic diffusion is usually much faster than system evolution, ancient fields cannot explain the present magnetization of planets, stars, and galaxies. Instead, self-sustaining dynamos, which convert fluid motion into magnetic energy, offer the most robust explanation. Numerical magnetohydrodynamic simulations are essential to understanding this phenomenon. This thesis uses numerical models of self-excited dynamos in two contexts: the interstellar medium (ISM) and the interiors of gas giant planets. First, I use 3D MHD simulations with the Pencil Code to study magnetic growth from irrotational, subsonic expansion flows, a simplified representation of supernova-driven motions in the ISM. These curl-free flows mimic stellar explosions and winds, drive turbulence, and seed magnetic amplification. The second part examines planetary dynamos. I outline the properties of planetary magnetic fields and their modeling through convection in spherical shells. Although many exoplanets are known, their magnetic fields remain difficult to detect, but may be observable through coherent radio emission with new low-frequency instruments. Using 3D dynamo simulations with the MagIC code, coupled to thermodynamic profiles from MESA-based evolution models, I study the magnetic evolution of cold gas giants. The models show a slow decline in field strength, a shift from multipolar to dipolar states, and clear evolutionary trends in dynamo behavior. I also investigate hot Jupiters, where strong irradiation alters convection and rotation. Most remain fast rotators, but massive, distant planets may enter different regimes. When heating is concentrated in outer layers, convection in the dynamo region weakens, reducing expected field strengths and helping explain the absence of confirmed detections in past radio surveys.