Silicon solar cells are the most established solar cell technology and are expected to dominate the market in the near future. As state-of-the-art silicon solar cells are approaching the Shockley–Queisser limit, stacking silicon solar cells with other photovoltaic materials to form multi-junction devices is an obvious pathway to further raise the efficiency. However, many challenges stand in the way of fully realizing the potential of silicon tandem solar cells because heterogeneously integrating silicon with other materials often degrades their qualities. Recently, above or near 30% silicon tandem solar cell has been demonstrated, showing the promise of achieving high-efficiency and low-cost solar cells via silicon tandem. This paper reviews the recent progress of integrating solar cell with other mainstream solar cell materials. The first part of this review focuses on the integration of silicon with III–V semiconductor solar cells, which is a long-researched topic since the emergence of III–V semiconductors. We will describe the main approaches—heteroepitaxy, wafer bonding and mechanical stacking—as well as other novel approaches. The second part introduces the integration of silicon with polycrystalline thin-film solar cells, mainly perovskites on silicon solar cells because of its rapid progress recently. We will also use an analytical model to compare the material qualities of different types of silicon tandem solar cells and project their practical efficiency limits.