  A graph is called 1-planar if there exists its drawing in the plane such that
each edge is crossed at most once. In this paper, we study 1-planar graph
joins. We prove that the join $G+H$ is 1-planar if and only if the pair $[G,H]$
is subgraph-majorized (that is, both $G$ and $H$ are subgraphs of graphs of the
major pair) by one of pairs $[C_3 \cup C_3,C_3], [C_4,C_4], [C_4,C_3],
[K_{2,1,1},P_3]$ in the case when both factors of the graph join have at least
three vertices. If one factor has at most two vertices, then we give several
necessary/sufficient conditions for the bigger factor.
