Replay's blog series delves into the mechanics of how its time travel debugger operates, detailing the process of recording, replaying, and analyzing a program to facilitate debugging. Unlike conventional debuggers, Replay's approach allows viewing a program's state at any point in time by leveraging the deterministic nature of browsers, which behave consistently given the same inputs and internal non-determinism. By efficiently recording inputs and selectively allowing behavior variability, Replay can reconstruct any point in the program's timeline with minimal overhead, offering a revolutionary speed and efficiency in debugging. The series also discusses the cooperation between Replay's backend and the replayed program to handle client requests during the inspection of recordings, emphasizing effective determinism's crucial role in this innovative debugging method.