The origin and progress of multicellularity, which is one of the crucial steps in the evolution of life, remains unclear and stringent phylogenetic reconstruction of the process is difficult. However, further theoretical considerations of the problem could be useful for the creation of a verifiable hypothesis. Sex as a ubiquitous biological phenomenon is usually considered as something entirely linked with reproduction. This is mostly true for modem multicellular organisms, but at the earliest stage of evolution of eukaryotes it was not so. At that time the sexual process had nothing to do with reproduction, and only later, sex and reproduction merged together. One of the aims of this paper is to consider the sexual process as a likely basis for the establishment of multicellularity and to discuss the early stages of evolution of the multicellularity from this perspective. It is suggested that mitotic reproduction of cells at different stages of the sexual cycle of unicellular ancestors might be the starting points for independent transition to multicellularity in different taxa. Numerous consequences of these transitions, including evolution of bisexuality and development of novel meiotic functions in animals, are discussed.