He graduated at Pembroke College, Cambridge in 1661,[1] and ten years later took the degree of MD at Leiden University, his thesis being Disputatio medico-physica de liquore nervoso.

He edited the Philosophical Transactions in 1678–1679, and in 1681 he published by request a descriptive catalogue of the rarities preserved at Gresham College, with which were printed some papers he had read to the Royal Society on the Comparative Anatomy of Stomachs and Guts.

He described nearly all the key differences of morphology of stem and root, showed that the flowers of the Asteraceae are built of multiple units, and correctly hypothesized that stamens are male organs.

Much of Grew's pioneering work with the microscope was contemporary with that of Marcello Malpighi (b.1628-d.1694), and the two reportedly borrowed freely from one another.

[2] Among his other publications were Seawater made Fresh (1684), the Nature and Use of the Salt contained in Epsom and such other Waters (1697), which was a rendering of his Tractatus de salis (1693), and Cosmologia Sacra (1701).