A Manhattan World (MW)  is composed of planar surfaces and parallel lines aligned with three mutually orthogonal principal axes. Traditional MW understanding algorithms rely on geometry priors such as the vanishing points and reference (ground) planes for grouping coplanar structures. In this paper, we present a novel single-image MW reconstruction algorithm from the perspective of non-pinhole cameras. We show that by acquiring the MW using an XSlit camera, we can instantly resolve co planarity ambiguities. Specifically, we prove that parallel 3D lines map to 2D curves in an XSlit image and they converge at an XSlit Vanishing Point (XVP). In addition, if the lines are coplanar, their curved images will intersect at a second common pixel that we call Coplanar Common Point (CCP). CCP is a unique image feature in XSlit cameras that does not exist in pinholes. We present a comprehensive theory to analyze XVPs and CCPs in a MW scene and study how to recover 3D geometry in a complex MW scene from XVPs and CCPs. Finally, we build a prototype XSlit camera by using two layers of cylindrical lenses. Experimental results on both synthetic and real data show that our new XSlit-camera-based solution provides an effective and reliable solution for MW understanding.