We review more than 10 yr of continuous monitoring of accreting X-ray pulsars with the all-sky Gamma-ray Burst Monitor (GBM) aboard the Fermi Gamma-ray Space Telescope. Our work includes data from the start of GBM operations in 2008 August, through to 2019 November. Pulsations from 39 accreting pulsars are observed over an energy range of 10-50 keV by GBM. The GBM Accreting Pulsars Program performs data reduction and analysis for each accreting pulsar and makes histories of the pulse frequency and pulsed flux publicly available. We examine in detail the spin histories, outbursts, and torque behaviors of the persistent and transient X-ray pulsars observed by GBM. The spin period evolution of each source is analyzed in the context of disk-accretion and quasi-spherical settling accretion-driven torque models. Long-term pulse frequency histories are also analyzed over the GBM mission lifetime and compared to those available from the previous Burst and Transient Source Experiment all-sky monitoring mission, revealing previously unnoticed episodes in some of the analyzed sources (such as a torque reversal in 2S 1845−024). We obtain new, or update known, orbital solutions for three sources. Our results demonstrate the capabilities of GBM as an excellent instrument for monitoring accreting X-ray pulsars and its important scientific contribution to this field.