Summary: In this paper, we propose and study the polar Orlicz-Minkowski problems, specifically, under what conditions on a nonzero finite measure \(\mu\) and a continuous function \(\varphi:(0,\infty)\to(0,\infty)\) there exists a convex body \(K\in\mathcal{K}_0\) such that \(K\) is an optimizer of the following optimization problems: \[ \inf/\sup\bigg\{\int_{S^{n-1}}\varphi(h_L)\mathrm{d}\mu:L\in\mathcal{K}_0\text{ and }|L^{\circ}|=\omega_n\bigg\}\ ? \] The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certain conditions on \(\varphi \), the existence of a solution is proved for a nonzero finite measure \(\mu\) on \(S^{n-1}\) which is not concentrated on any hemisphere of \(S^{n-1}\). Another part of this paper deals with the \(p\)-capacitary Orlicz-Petty bodies. In particular, the existence of the \(p\)-capacitary Orlicz-Petty bodies is established and the continuity of the \(p\)-capacitary Orlicz-Petty bodies is proved.