Explore a scientific lecture on the numerical simulations and gravitational wave memory of long gamma-ray burst jets, presented at the Warsaw colloquium for theoretical physics. Delve into the physics of gamma-ray bursts (GRBs), the most luminous explosions in the universe with luminosities ranging from 10^50 to 10^52 erg/s, and their origins in stripped-envelope massive star collapses. Learn about cutting-edge numerical simulations tracking relativistic jet propagation through progenitor stars and beyond breakout, while discovering how gravitational wave emissions from ultra-relativistic jets offer new insights where electromagnetic observations fall short. Understand how future gravitational wave detectors like LISA, BBO, DECIGO, and ALIA could revolutionize our understanding of jet evolution by detecting these signals, complementing traditional electromagnetic observations for a comprehensive view of these cosmic phenomena.