In 1952 Chandler defined the so-called record times and record values and gave groundwork for a mathematical theory of records. For six decade beginning his pioneering work there appeared about 600 papers and some monographs devoted to different aspects of the theory of records. This theory relies largely on the theory of order statistics and is especially closely connected to extreme order statistics. Records are very popular because they arise naturally in many fields of studies such as climatology, sports, medicine, traffic, industry and so on. The records as such are memorials of their time. The annals of records reflect the progress in science and technology and enable us to study the evaluation of mankind on the basic of record achievements in various areas of its activity. A large number of record data saved for a long time inspirited the appearance of different mathematical models reflecting the corresponding record processes and forecasting the future record results.