Ageing research benefits from the study of accelerated ageing syndromes such as Hutchinson-Gilford 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.