This paper investigates gate-tunable topological phases in superlattice-modulated bilayer graphene (SL-BLG). The study explores how the band topology and interaction-induced symmetry-broken phases in SL-BLG are controlled by tuning the displacement field and the shape and strength of the superlattice potential. Using analytic perturbative analysis and numerical simulations, the authors demonstrate that topological flat bands are favored by a honeycomb-lattice-shaped potential. The robustness of these topological bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, the system exhibits phase transitions between quantum anomalous Hall (QAHI), trivial insulator, and metallic states. The authors present mean-field phase diagrams at filling factor ν=1 and discuss the potential for realizing QAHI and fractional Chern insulators using dielectric patterning or adjacent moiré materials. The study shows that the first conduction miniband is topologically nontrivial when the superlattice potential minima form a honeycomb lattice. At ν=1, the system is a valley-polarized QAHI over a large parameter range. The phase diagram in the V₀-φ parameter space reveals that the topological region is centered at φ=0 for the first conduction miniband and φ=π/3 for the first valence miniband. The width of the topological region decreases with increasing |V₀| and increases with smaller lattice constants. The results suggest that QAHI states can be routinely realized in honeycomb-superlattice potential modulated BLG without fine-tuning. The paper also discusses the implications of the results for other systems and highlights the potential for observing fractional Chern insulators at fractional fillings within the QAHI regions. The study provides insights into the role of Berry curvature and the effects of superlattice modulation on the electronic structure and topological properties of SL-BLG. The findings have important implications for the experimental realization of topological phases in two-dimensional materials.This paper investigates gate-tunable topological phases in superlattice-modulated bilayer graphene (SL-BLG). The study explores how the band topology and interaction-induced symmetry-broken phases in SL-BLG are controlled by tuning the displacement field and the shape and strength of the superlattice potential. Using analytic perturbative analysis and numerical simulations, the authors demonstrate that topological flat bands are favored by a honeycomb-lattice-shaped potential. The robustness of these topological bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, the system exhibits phase transitions between quantum anomalous Hall (QAHI), trivial insulator, and metallic states. The authors present mean-field phase diagrams at filling factor ν=1 and discuss the potential for realizing QAHI and fractional Chern insulators using dielectric patterning or adjacent moiré materials. The study shows that the first conduction miniband is topologically nontrivial when the superlattice potential minima form a honeycomb lattice. At ν=1, the system is a valley-polarized QAHI over a large parameter range. The phase diagram in the V₀-φ parameter space reveals that the topological region is centered at φ=0 for the first conduction miniband and φ=π/3 for the first valence miniband. The width of the topological region decreases with increasing |V₀| and increases with smaller lattice constants. The results suggest that QAHI states can be routinely realized in honeycomb-superlattice potential modulated BLG without fine-tuning. The paper also discusses the implications of the results for other systems and highlights the potential for observing fractional Chern insulators at fractional fillings within the QAHI regions. The study provides insights into the role of Berry curvature and the effects of superlattice modulation on the electronic structure and topological properties of SL-BLG. The findings have important implications for the experimental realization of topological phases in two-dimensional materials.