The paradigm of cellular systems as deterministic machines has long guided our understanding of biology. Advancements in technology and methodology, however, have revealed a world of stochasticity, challenging the notion of determinism. Here, we explore the stochastic behavior of multi-protein complexes, using the DNA replication system (replisome) as a prime example. The faithful and timely copying of DNA depends on the simultaneous action of a large set of enzymes and scaffolding factors. This fundamental cellular process is underpinned by dynamic protein-nucleic acid assemblies that must transition between distinct conformations and compositional states. Traditionally viewed as a well-orchestrated molecular machine, recent experimental evidence has unveiled significant variability and heterogeneity in the replication process. In this review, we discuss recent advances in single-molecule approaches and single-particle cryo-EM, which have provided insights into the dynamic processes of DNA replication. We comment on the new challenges faced by structural biologists and biophysicists as they attempt to describe the dynamic cascade of events leading to replisome assembly, activation, and progression. The fundamental principles uncovered and yet to be discovered through the study of DNA replication will inform on similar operating principles for other multi-protein complexes.