Cryogenic solid para-hydrogen (p-H2) exhibits pronounced quantum effects, enabling unique experiments that are typically not possible in noble-gas matrices. The diminished cage effect facilitates the production of free radicals via in situ photolysis or photoinduced reactions. Electron bombardment during deposition readily produces protonated and hydrogenated species, such as polycyclic aromatic hydrocarbons, that are important in astrochemistry. In addition, quantum diffusion delocalizes hydrogen atoms in solid p-H2, allowing efficient H atom reactions with astrochemical species and introducing new concepts in astrochemical models. Some H atom reactions display anomalous temperature behaviors, highlighting the rich chemistry in p-H2. The investigation on quantum diffusion of heavier atoms and molecules is also important for our understanding of the chemistry in interstellar ice. Additionally, matrix shifts of electronic transitions of polycyclic aromatic hydrocarbons in p-H2 are less divergent than those in solid Ne such that systematic measurements in p-H2 might help in the assignment of diffuse interstellar bands.