Ageing research benefits from the study of accelerated ageing syndromes such as HutchinsonGilford progeria syndrome (HGPS), characterized by the early appearance of symptoms normally associated with advanced age. Most HGPS cases are caused by a mutation in the gene LMNA, which leads to the synthesis of a truncated precursor of lamin A known as progerin that lacks the target sequence for the metallopotease FACE-1/ZMPSTE24 and remains constitutively farnesylated. The use of Face-1/Zmpste24-deficient mice allowed us to demonstrate that accumulation of farnesylated prelamin A causes severe abnormalities of the nuclear envelope, hyper-activation of p53 signalling, cellular senescence, stem cell dysfunction and the development of a progeroid phenotype. The reduction of prenylated prelamin A levels in genetically modified mice leads to a complete reversal of the progeroid phenotype, suggesting that inhibition of protein farnesylation could represent a therapeutic option for the treatment of progeria. However, we found that both prelamin A and its truncated form progerin can undergo either farnesylation or geranylgeranylation, revealing the need of targeting both activities for an efficient treatment of HGPS. Using Face-1/Zmpste24-deficient mice as model, we found that a combination of statins and aminobisphosphonates inhibits both types of modifications of prelamin A and progerin, improves the ageing-like symptoms of these mice and extends substantially their longevity, opening a new therapeutic possibility for human progeroid syndromes associated with nuclear-envelope defects. We discuss here the use of this and other animal models to investigate the molecular mechanisms underlying accelerated ageing and to test strategies for its treatment.