The recent association between IC-170922A and the blazar TXS0506+056 highlights the importance of real-time observations for identifying possible astrophysical neutrino sources. Thanks to its near-100% duty cycle, 4$pi$ steradian field of view, and excellent sensitivity over many decades of energy, IceCube is well suited both to generate alerts for follow-up by other instruments and to rapidly follow up alerts generated by other instruments. Detection of neutrinos in coincidence with transient astrophysical phenomena serves as a smoking gun for hadronic processes and supplies essential information about the identities and mechanisms of cosmic-ray accelerators. In 2016, the IceCube Neutrino Observatory established a pipeline to rapidly search for neutrinos from astrophysical transients on timescales ranging from a fraction of a second to multiple weeks. Since then, 67 dedicated analyses have been performed searching for associations between IceCube neutrinos and astrophysical transients reported by radio, optical, X-ray, and gamma-ray instruments in addition to searching for lower energy neutrino signals in association with IceCubes own high-energy alerts. We present the event selection, maximum likelihood analysis method, and sensitivity of the IceCube real-time pipeline. We also summarize the results of all follow-up analyses to date.