The Golgi apparatus is an intracellular organelle that modifies cargo, which is transported extracellularly through the nucleus, endoplasmic reticulum, and plasma membrane in order. First, the general function of the Golgi is reviewed and, then, Golgi stress signaling is discussed. In addition to the six main Golgi signaling pathways, two pathways that have been increasingly reported in recent years are described in this review. The focus then shifts to neurological disorders, examining Golgi stress reported in major neurological disorders, such as Alzheimer’s disease, Parkinson’s disease, and Huntington’s disease. The review also encompasses findings related to other diseases, including hypomyelinating leukodystrophy, frontotemporal spectrum disorder/amyotrophic lateral sclerosis, microcephaly, Wilson’s disease, and prion disease. Most of these neurological disorders cause Golgi fragmentation and Golgi stress. As a result, strong signals may act to induce apoptosis.