Summary: Given a set of points \(P\) and axis-aligned rectangles \(\mathcal{R}\) in the plane, a point \(p\in P\) is called exposed if it lies outside all rectangles in \(\mathcal{R}\). In the max-exposure problem, given an integer parameter \(k\), we want to delete \(k\) rectangles from \(\mathcal{R}\) so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in \(\mathcal{R}\) are translates of two fixed rectangles. However, if \(\mathcal{R}\) only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For range space defined by general rectangles, we present a simple \(O(k)\) bicriteria approximation algorithm; that is by deleting \(O( k^2)\) rectangles, we can expose at least \(\Omega(1/k)\) of the optimal number of points.