In this interesting article, the authors initiate a program to resolve the existence of closed prescribed mean curvature hypersurfaces, based on extending their min-max theory developed in [X. Zhou and J. J. Zhu, Invent. Math. 218, No. 2, 441–490 (2019; Zbl 1432.53086)] for constant mean curvature hypersurfaces. In particular, in Theorem 0.1 is proved that there exists a closed hypersurface of prescribed mean curvature \(h\) for a generic set of prescription functions \(h\). More precisely, if \(M^{n+1}\) is a smooth, closed Riemannian manifold with \(3\leq n+1\leq 7\), then there is an open dense set \(S\subset C^{\infty}(M)\) of prescription functions \(h\), for which there exists a nontrivial, smooth, closed, almost embedded hypersurface \(\Sigma ^n\) of prescribed mean curvature \(h\). The dimension restriction comes from the regularity theory for stable minimal hypersurfaces and is typical of variational methods for hypersurfaces. Other first author papers directly connected to these results are [X. Zhou, J. Differ. Geom. 105, No. 2, 291–343 (2017; Zbl 1367.53054); D. Ketover and X. Zhou, J. Differ. Geom. 110, No. 1, 31–71 (2018; Zbl 1396.53004)].