  In this paper, we study generic conformally flat hypersurfaces in the
Euclidean $4$-space $\mathbb{R}^4$ using the framework of M\"{o}bius geometry.
First, we classify locally the generic conformally flat hypersurfaces with
closed M\"obius form under the M\"obius transformation group of $\mathbb{R}^4$.
Such examples come from cones, cylinders, or rotational hypersurfaces over the
surfaces with constant Gaussian curvature in $3$-spheres, Euclidean $3$-spaces,
or hyperbolic $3$-spaces, respectively. Second, we investigate the global
behavior of the generic conformally flat hypersurface and give some integral
formulas about these hypersurfaces.
