We will discuss modular compactifications of \(M_{g,n}\) (the moduli space of smooth curves) and their birational geometry within the framework of the Hassett-Keel program. We classify the open substacks of canonically polarized curves with nodes, cusps, and tacnodes having a proper good moduli space. Using the \(S\)- and \(\Theta\)-completeness criteria, we transform the problem into a combinatorial one where compactifications and flips can be described using cluster algebra theory. This approach yields a complete description of the \(\mathbb{Q}\)-factorialization fan of \(\overline{M}_{g,n}(7/10)\) as a cluster fan.