He specialized in tropical flora, with emphasis on plants from Mexico and Central America.

[1] He was an authority on the genus Senecio and noted for his work at the Missouri Botanical Garden.

[2][3] In 1894 he went to Harvard University studying and working in the Gray Herbarium until 1899 when he earned his master's degree.

[2] He began working at the Missouri Botanical Garden as curator in 1913,[4] remaining there until his retirement in 1943.

[2] Beginning in 1968, the "Jesse M. Greenman Award" is awarded by the "Missouri Botanical Garden Herbarium" in his honor for an academic paper "...judged best in vascular plant or bryophyte systematics based on a doctoral dissertation that was published during the previous year".