Cultural heritage conservation increasingly relies on non-destructive techniques and imaging methods based on the absorption or scattering of photons (X or γ-rays) or neutrons. While these techniques offer excellent imaging capabilities and material identification, their penetration depth becomes insufficient for large or dense objects, such as compact stone or metal artifacts. Moreover, their application is often constrained by logistical constraints, as they are typically limited to relatively small objects that can be transported to dedicated imaging facilities. Although x-ray computed tomography systems and portable fast neutron sources have begun to enable in situ studies, their use remains restricted by radiation hazard regulations. Muon tomography offers a promising alternative, overcoming these limitations due to its high penetration power, lack of radiation hazards, and the potential for portable detector designs. In this work, we first discuss future applications of muon imaging in cultural heritage preservation. We then present simulation studies focused on statue imaging to determine the conditions under which the two existing muography techniques—absorption and scattering—are most effective. Finally, we outline the technological and methodological advancements required to establish muography as a reliable tool for cultural heritage applications. This contribution is part of the proceedings of the Muographers Workshop 2024.