The picobirnaviruses (Picobirnaviridae, Picobirnavirus, PBVs) are currently thought to be animal viruses, as they are usually found in animal stool samples. However, no animal model or cell culture for their propagation has yet been found. In 2018, a hypothetical assumption about PBVs belonging to prokaryotic viruses was put forward and experimentally substantiated. This hypothesis is based on the presence of Shine–Dalgarno sequences in the genome of all PBVs before three reading frames (ORF) at the ribosomal binding site, with which the prokaryotic genome is saturated, while in the eukaryotic genome such regions occur with low frequency. The genome saturation with the Shine–Dalgarno sequences, as well as the preservation of this saturation in the progeny, according to scientists, allows us to attribute PBVs to prokaryotic viruses. On the other hand, there is a possibility that PBVs belong to viruses of eukaryotic hosts – fungi or invertebrates, since PBV-like sequences similar to the genome of fungal viruses from the families of mitoviruses and partitiviruses have been identified. In this regard, the idea arose that, in terms of reproduction mode, PBVs resemble fungal viruses. The divergence of views on the true PBV host(s) has sparked discussions among scientists and required further research to elucidate their nature. The review highlights the results of the search for a PBV host. The reasons for the occurrence of atypical sequences among the PBV genome sequences that use an alternative mitochondrial code of lower eukaryotes (fungi and invertebrates) for the translation of viral RNA-dependent RNA polymerase (RdRp) instead of the standard genetic code are analyzed. The purpose of the review was to collect arguments in support of the hypothesis about the phage nature of PBVs and to find the most realistic explanation of the reasons for identifying non-standard genomic sequences for PBVs. Based on the hypothesis about the genealogical relationship of PBVs with RNA viruses from other families with similar segmented genomes, such as Reoviridae, Cystoviridae, Totiviridae and Partitiviridae, virologists support the assumption of a decisive role in the origin of atypical PBV-like reassortment strains between PBVs and viruses of the listed families. The collected arguments given in this review indicate a high probability of a phage nature of PBVs. The data presented in the review show that the belonging of PBV-like progeny to prokaryotic or eukaryotic viruses is determined not only by its genome saturation level with a prokaryotic motif, standard or mitochondrial genetic code. The primary structure of the gene encoding the viral capsid protein responsible for the presence or absence of specific proteolytic properties of the virus that determine its ability for independent horizontal transmission into new cells may also be a decisive factor.