Progeria syndromes have in common a premature aging phenotype and increased genome instability. The susceptibility to DNA damage arises from a compromised repair system, either in the repair proteins themselves or in the DNA damage response pathways. The most severe progerias stem from mutations affecting lamin A production, a filamentous protein of the nuclear lamina. Hutchinson-Gilford progeria syndrome (HGPS) patients are heterozygous for a LMNA gene mutation while Restrictive Dermopathy (RD) individuals have a homozygous deficiency in the processing protease Zmpste24. These mutations generate the mutant lamin A proteins progerin and FC-lamina A, respectively, which cause nuclear deformations and chromatin perturbations. Genome instability is observed even though genome maintenance and repair genes appear normal. The unresolved question is what features of the DNA damage response pathways are deficient in HGPS and RD cells. Here we review and discuss recent findings which resolve some mechanistic details of how the accumulation of progerin/FC-lamin A proteins may disrupt DNA damage response pathways in HGPS and RD cells. As the mutant lamin proteins accumulate they sequester replication and repair factors, leading to stalled replication forks which collapse into DNA double-strand beaks (DSBs). In a reaction unique to HGPS and RD cells these accessible DSB termini bind Xeroderma pigmentosum group A (XPA) protein which excludes normal binding by DNA DSB repair proteins. The bound XPA also signals activation of ATM and ATR, arresting cell cycle progression, leading to arrested growth. In addition, the effective sequestration of XPA at these DSB damage sites makes HGPS and RD cells more sensitive to ultraviolet light and other mutagens normally repaired by the nucleotide excision repair pathway of which XPA is a necessary and specific component.