Replication stress (RS) is a hallmark of cancer cells that is associated with increased genomic instability. RS occurs when replication forks encounter obstacles along the DNA. Stalled forks are signaled by checkpoint kinases that prevent fork collapse and coordinate fork repair pathways. Fork restart also depends on chromatin remodelers to increase the accessibility of nascent chromatin to recombination and repair factors. In this review, we discuss recent findings on the causes and consequences of RS, with a focus on endogenous replication impediments and their impact on fork velocity. We also discuss recent studies on the interplay between stalled forks and innate immunity, which extends the RS response beyond cell boundaries and opens new avenues for cancer therapy.