Canadian by birth, Glover spent most of his life in China and the United States. A graduate of the University of Toronto, New York Missionary Training College, and New York University Medical College (M.D.), he was appointed a medical missionary to China in 1894 by the Christian and Missionary Alliance (C&MA). He lived through the Boxer rebellion, when many missionaries were killed and others were forced to flee the country. In response to the crescendo of calls to quit China, Glover wrote a stirring defense of missionary efforts there entitled "Shall Suffering and Danger Halt Our Missionary Work?" His service with the C&MA in China continued until 1913.
During his years in China he was ordained, married Caroline Robbins Prentice, and founded two educational institutions. In 1913 he was appointed C&MA foreign missions secretary. In 1921 Moody Bible Institute recruited him to serve as director of missionary studies, a position he occupied until 1926, during which time he wrote the Progress of World-Wide Missions (1924), one of the most widely used mission histories ever written; it was translated into multiple languages. In 1926 he became a missionary administrator for the China Inland Mission (CIM), serving as assistant home director (1926-1929) and as home director (1930-1943). He retired in Germantown, Pennsylvania, in 1943.