Particle-in-cell (PIC) methods have achieved widespread recognition as simple and flexible approaches to model collisionless plasma physics in fully kinetic simulations of astrophysical environments. However, in many situations the standard PIC algorithm must be extended to include macroscopic effects in microscale simulations. For plasmas subjected to shearing or expansion, shearing-box and expanding-box methods can be incorporated into PIC to account for these global effects. For plasmas subjected to local acceleration in confined regions of space, a leaky-box method can allow closed-box PIC simulations to account for particle escape from the accelerator region. In this work, we review and improve methods to include shearing, expansion, and escape in PIC simulations. We provide the numerical details of how Maxwell’s equations and the particle equations of motion are solved in each case, and introduce generalized Boris-like particle pushers to solve the momentum equation in the presence of extra forces. This work is intended to serve as a comprehensive reference for the implementation of shearing-box, expanding-box, and leaky-box algorithms in PIC.