This article is the first part of the review of publications on the problem of increasing the service life and improving the reliability of fuel assemblies (FA) and fuel rods (FR). In the next issues of the journal, Part 2 Dynamic interactions between the coolant flow and FAs and Part 3 Prediction of vibroacoustic resonances in the reactor cores of VVER-based nuclear power of this review will be published. This review part presents the results from investigations into the causes and mechanisms of FR failures, in which radioactive materials (gaseous fission products and volatile elements, in particular, krypton, xenon, iodine, and cesium) escape from the fuel pellet into the reactor primary coolant circuit. It is shown that the nuclear fuel depressurization level is influenced by all stages of the product life cycle, including design, manufacture, and operation of FAs. In particular, during operation, FA vibrations have an effect on the nuclear fuel depressurization level. As is well-known, an FA is a hydroelastic oscillatory system consisting of two interacting subsystems: a mechanical one and a hydrodynamic one. The FA vibration is due to the dynamic processes occurring in these subsystems. It is noted that the hydrodynamic subsystem has been studied to a rather insufficient extent, which is due to complexity of describing the processes through which the random hydrodynamic loads applied to the streamlined surfaces are produced, as well as the influence of flow thermal-hydraulic and acoustic characteristics on the occurrence of self-excited oscillations. Based on the defective FA operation data, the service life of leaky fuel rods and their linear heat generation rates are estimated. The evolutions of fuel operation conditions and fuel design changes are described. The available recommendations on optimizing FA designs developed taking into account the experience gained from operation of the reactors and the results of the accomplished fretting wear investigations are mentioned. It is shown that all who manufacture and operate nuclear fuel take efforts aimed at improving its quality, because it is the key indicator characterizing the vendor of fuel and nuclear power plants in the world market. Achieving longer fuel campaigns and higher burnup values while keeping or even improving the safety level are the most important criteria for nuclear fuel quality. Currently, the project called Nuclear Fuel Zero Failure Level is in the stage of implementation and obtaining the first results of joint activities of all participants.