This article brieflyintroduces collaboration and cooperation-competition networksacross many fields of practical sciences. In the sectionpresenting the earlier empirical investigations, the most famousinvestigations on Hollywood movie actor collaboration network andthe scientific paper co-author network are introduced. In thesection about distribution of the act size and act degree, the twokinds of bipartite graph degrees, the empirical investigations andthe proposed collaboration network evolution models by USA RDPgroup and Chinese Yangzhou University group are introduced. In thesection concerned with correlation between assortativity and actdegree, the definitions of weighted and unweighted assortativity,and the empirical as well as the model studies on correlationbetween assortativity and act degree are summarized. In thesection about resource-allocation method of the bipartite graphprojection, the recent bipartite graph projection method anddefinition of edge weight are briefly presented based on the ideaof resource-allocation. In the section about the recent empiricalinvestigations on collaboration networks, the collaborationnetwork descriptions and the corresponding empiricalinvestigations are summarized about the systems of urban publictraffic, railway transportation, scientific research projects, andlanguages. In the last section concerned with thecooperation-competition networks and its description vianode-weight, the cooperation-competition network descriptions andempirical investigations on the systems of enterprise competition,movie market, student election of courses, student book borrowingand fruit nutritive factors are presented, and 44 selectivereferences are listed at the end of this paper.