Edge intelligence is anticipated to underlay the pathway to connected intelligence for 6G networks, but the organic confluence of edge computing and artificial intelligence still needs to be carefully treated. To this end, this article discusses the concepts of edge intelligence from the semantic cognitive perspective. Two instructive theoretical models for edge semantic cognitive intelligence (ESCI) are first established. Afterwards, the ESCI framework orchestrating deep learning with semantic communication is discussed. Two representative applications are present to shed light on the prospect of ESCI in 6G networks. Some open problems are finally listed to elicit the future research directions of ESCI.