Galaxies grow alongside central supermassive black holes (SMBHs) through fueling and feedback. However, the origins of this coevolution remain unclear and vary across modeling frameworks. Using semianalytic models (SAMs), we trace SMBH mass assembly acrossM_BH∼10⁶⁻¹⁰M_⊙. We find significant discrepancies between observations and physics-based models of the local black hole mass function (BHMF), likely from differences in the stellar mass function and scaling relations used to infer the BHMF. Most physics-based models agree atz∼1–4 and broadly match the JWST broad-line active galactic nucleus (AGN) BHMFs atz=4–5. These models also reproduce the observed bolometric AGN luminosity evolution, except the SAMDark Sage, which predicts an excess. Interestingly, this pronounced “knee” in the bolometric AGN luminosity function predicted byDark SagearoundL_bol∼10⁴⁶erg s⁻¹is consistent with the inferred abundance and luminosity of “little red dots” atz=5–6, under the assumption that they are powered entirely by AGN activity. In contrast to other models,Dark Sagedeploys multiple growth channels for SMBHs that include mergers, hot-mode accretion, merger-driven cold-accretion, and secular-instability-driven accretion. We analyze the black hole mass buildup and accretion histories inDark Sage, which, unlike other models, also allows for super-Eddington accretion, and we find that, on average, SMBHs primarily grow through secular disk instabilities and merger-driven cold gas accretion modes. We also find that black hole mergers contribute the majority of the growth of ∼60% of the total mass budget only for the most massive SMBHs byz= 0.