Well-known theories of aging suggest that a certain metabolic defect negatively affects vital activity of the cell, be it oxidative stress, the accumulation of lesions in DNA, the exhaustion of telomeres, or distorted epigenetic processes. The theory of aging considered in the review postulates that an accumulation of progerin on the inner side of the nuclear envelope underlies the above defects. Progerin is a defective precursor of the lamin A nuclear matrix protein in which the C-terminal cysteine, which is removed normally, is retained and modified with a hydrophobic oligoisoprene chain. Progerin molecules attach with their hydrophobic processes to the inner membrane of the nuclear envelope, pushing away the adjacent fibrils of the nuclear matrix and the chromatin periphery. This changes the morphology and shape of the nucleus and alters the properties of the nuclear envelope and pore complexes embedded in it. As progerin accumulates in the nucleus, structural distortions increase in the nucleus, further distorting the nuclear-cytoplasmic transport of macromolecules and leading to the above defects in cell metabolism. This leads to increasing cell death and aging of the body over time. This mechanism of aging has been identified in patients with Hutchinson-Gilford progeria syndrome (HGPS). Mass progerin production in HGPS is caused by the point mutation c.1824C→T in exon 11 of the LMNA gene, which codes for lamins A and C. The mutation stimulates non-standard splicing of the primary transcript during the formation of the lamin A precursor mRNA, thus causing progerin production. Children with progeria who have received the mutation from one of their parents age rapidly and die before 15 years of age. Approaches to progeria treatment are aimed at preventing the formation of progerin or destroying the progerin that has already accumulated. In the latter case, a promising strategy is to use rapamycin or its analogs and other substances and techniques that activate autophagy to purify the cell from progerin. Although in much smaller amounts, progerin is found in progeria-free people and may therefore play a role in natural aging. A maximum age that a person can reach is possible to estimate by taking account of the role that progerin plays in telomere shortening. Encouraging preliminary results achieved in purifying cells from progerin provide a means to develop an optimal procedure for periodic purification of the human body from progerin in order to reduce the rate of aging.