This invention provides bioreactors having a selectively permeable porous material with an open pore structure, useful for producing products including hydrogen gas, biomass, chemicals, and pharmaceuticals. The porous materials are utilized, for example, as one or more portions of or entire walls, covers, floors, filters, windows, or tubes of the bioreactors. This invention provides bioreactors comprising porous materials that are aerogels, xerogels, or sol-gel glasses, including silica aerogels. The selectively permeable porous materials are gas-permeable, and in addition optionally photopermeable, transparent, hydrophobic, and/or capable of functioning as sterile barriers. This invention provides methods for culturing cells and organisms employing the bioreactors of the invention. This invention further provides methods for producing gaseous products, including hydrogen, biomass, chemicals, and pharmaceuticals employing the bioreactors of the invention.