In this expository paper we revise some extensions of Kuratowski planarity criterion, providing a link between the embeddings of infinite graphs without accumulation points and the embeddings of finite graphs with some
distinguished vertices in only one face. This link is valid for any surface and for some pseudosurfaces. On the one hand, we present some key ideas that are not easily accessible. On the other hand, we state the relevance
of infinite, locally finite graphs in practice and suggest some ideas for future research
