The solar corona is so hot that its particles can overcome the sun's gravitational field and escape into outer space where they form the fast-flowing solar wind. Dynamical processes in the corona and solar wind as well as the interaction of the solar wind with the Earth's magnetic field lead to shocks. These shocks move through a medium that is so dilute that binary collisions between particles are negligible compared to collective particle interactions with the macroscopic electromagnetic fields, which are induced by the plasma currents. Shocks are important for plasma heating in the solar corona and for dynamical processes in the solar wind and the Earth's magnetosphere. Their collisionless nature lets them behave differently from for example hydrodynamic shocks in dense gases or liquids. We study with particle-in-cell (PIC) simulations the evolution of plasma shocks in nonuniform magnetized plasma. We model subcritical fast magnetosonic shocks, which are important structures in the solar corona and are widely observed in the solar wind. Even the Earth's bow shock can become subcritical if the solar wind speed is particularly low. Subcritical shocks are time-stationary in their rest frame and have a Mach number below 2-3 relative to the relevant plasma density wave. The transition layer of subcritical shocks is narrow, which facilitates its detection by satellites and in plasma experiments. Due to their narrow transition layer and rapid formation time, they can be simulated at a reasonable computational cost in PIC simulations that resolve two spatial dimensions. We focus on aspects like shock vibrations, drift instabilities that affect the shock transition layer, the collapse and reformation of the shocks, and the interaction of radial shocks with spatially uniform magnetic fields.