In this talk, we will discuss a proof of the asymptotic multipartite version of the Alon-Yuster theorem. That is, if $kgeq 3$ is an integer, $H$ is a $k$-colorable graph and $gamma>0$ is fixed, then for sufficiently large n and for every balanced $k$-partite graph $G$ on $kn$ vertices with each of its corresponding ${kchoose 2}$ bipartite subgraphs having minimum degree at least $frac{k-1}{k}n+gamma n$, the graph $G$ has a subgraph consisting of $lfloor kn/|V(H)|rfloor$ vertex-disjoint copies of $H$. This is joint work with Jozef Skokan, London School of Economics.