This article deals with the problem of cloning and ethical issues surrounding it. The aim of this work is to explore ethical issues that arise in the process of cloning. The relevance of this issue is growing because cloning of animals and potentially humans has been under investigation nowadays. We have examined the ethical aspects of this issue as well as the social ones. We have studied principal arguments for and against cloning. As you know, the greatest problem in the society of all time in the field of genetic engineering is the question of human cloning. In spite of the fact that results may be promising, the majority of the scientific, social and religious organizations are opposed to cloning. Concerns about it still exist due to the fact that changes in genome can lead not only to changes in physical appearance, but also to changes in physiology and psychology.