The development of the safest and, at the same time, efficient methods of cataract surgery, is not only a topical task of medical science and practice, but also, taking the demographic situation into account, a solution to a social problem. The article describes the main achievements of academician S. N. Fyodorov's school in the field of cataract surgery with intraocular lense (IOL) implantation. Special attention is paid to the key components of cataract extraction technique named "small incision surgery", which is based upon the use of ultrasmall surgical approaches with self-sealing ability and no need for suturing. The main advantages and disadvantages of various types of cataract lense fragmentation, including ultrasound emulsification, mechanic and hydraulic fragmentation, and laser destruction, are described. Topical issues concerning cataract extraction technique under the conditions of complicating ophthalmopathology including the weakness of ciliary zonule system, high-degree myopia, glaucoma, pseudoexfoliative syndrome, small pupil, past injuries and eye surgery, are outlined. The paper also reflects a new qualitative step in the development of intraocular aphakia correction technique under modern conditions. Basic requirements to design parameters and IOL materials are determined from the position of reestablishing the accommodative function and fine visual functions. Ways of IOL design improvement are described especially for their application in non-standard and complicated cases.