Parent, hierarchical, and metal-modified hierarchical zeolite Y were investigated as heterogeneous catalysts in the R-(+)-limonene epoxidation, a catalytic route for synthesizing precursors of bio-polycarbonates, an alternative to isocyanate polyurethanes. The fresh catalysts underwent detailed characterization using XRD, N2 physisorption, TEM, SEM-EDX, pyridine-FTIR, NH3-TPD, CO2-TPD, UV–Vis-DRS, and solid-state NMR. Spent materials were investigated by TPO-MS and TGA, confirming low coke formation on the catalytic surface. The most active material was K–Sn-modified dealuminated zeolite Y, reflected in a high turnover frequency (TOF) of 96 h−1. This material exhibited the lowest Brønsted to Lewis acidity ratio (0.1), the highest mesoporosity fraction (43%), and the lowest total surface area (465 m2 g−1). Aprotic polar solvents with high polarity and medium donor capacity appeared suitable for limonene epoxidation. Limonene conversion of ca. 97% was reached at 70 °C, H2O2: limonene molar ratio = 7, and acetonitrile as a solvent, while selectivity to total monoepoxides exhibited values up to 96% under different reaction conditions. Hydration of internal epoxides to limonene diol was favored at high temperatures and high H2O2/limonene molar ratios. The efficiency of H2O2 reached maximum values of about 85% at low H2O2 amounts, while no significant influence was observed for temperature, catalyst amount, and the initial concentration of limonene. A plausible reaction mechanism was proposed for the R-(+)-limonene epoxidation with H2O2 based on the experimental findings.