Cells slow replication in response to DNA damage. This slowing was the first DNA damage checkpoint response discovered and its study led to the discovery of the central checkpoint kinase, Ataxia Telangiectasia Mutated (ATM). Nonetheless, the manner by which the S-phase DNA damage checkpoint slows replication is still unclear. The checkpoint could slow bulk replication by inhibiting replication origin firing or slowing replication fork progression, and both mechanisms appear to be used. However, assays in various systems using different DNA damaging agents have produced conflicting results as to the relative importance of the two mechanisms. Furthermore, although progress has been made in elucidating the mechanism of origin regulation in vertebrates, the mechanism by which forks are slowed remains unknown. We review both past and present efforts towards determining how cells slow replication in response to damage and try to resolve apparent conflicts and discrepancies within the field. We propose that inhibition of origin firing is a global checkpoint mechanism that reduces overall DNA synthesis whenever the checkpoint is activated, whereas slowing of fork progression reflects a local checkpoint mechanism that only affects replisomes as they encounter DNA damage and therefore only affects overall replication rates in cases of high lesion density.