The natural products synthesized by organisms that were living a long time ago gave rise to their molecular fossils. These can consist of either the original unchanged compounds or they may undergo peripheral transformations in which their skeletons remain intact. In cases when molecular fossils can be traced to their organismic source, they are termed "geological biomarkers".This contribution describes apolar and polar molecular fossils and, in particular biomarkers, along the lines usually followed in organic chemistry textbooks, and points to their bioprecursors when available. Thus, the apolar compounds are divided in linear and branched alkanes followed by alicyclic compounds and aromatic and heterocyclic molecules, and, in particular, the geoporphyrins. The polar molecular fossils contain as functional groups or constituent units ethers, alcohols, phenols, carbonyl groups, flavonoids, quinones, and acids, or are polymers like kerogen, amber, melanin, proteins, or nucleic acids. The final sections discuss the methodology used and the fundamental processes encountered by the biomolecules described, including diagenesis, catagenesis, and metagenesis.