The compound BMAA (β-N-methylamino-L-alanine) has been postulated to play a significant role in four serious neurological human diseases: Amyotrophic Lateral Sclerosis/Parkinsonism Dementia Complex (ALS/PDC) found on Guam, and ALS, Parkinsonism, and dementia that occur globally. ALS/PDC with symptoms of all three diseases first came to the attention of the scientific community during and after World War II. It was initially associated with cycad flour used for food because BMAA is a product of symbiotic cycad root-dwelling cyanobacteria. Human consumption of flying foxes that fed on cycad seeds was later suggested as a source of BMAA on Guam and a cause of ALS/PDC. Subsequently, the hypothesis was expanded to include a causative role for BMAA in other neurodegenerative diseases including Alzheimer’s disease (AD) through exposures attributed to proximity to freshwaters and/or consumption of seafood due to its purported production by most species of cyanobacteria. The hypothesis that BMAA is the critical factor in the genesis of these neurodegenerative diseases received considerable attention in the medical, scientific, and public arenas. This review examines the history of ALS/PDC and the BMAA-human disease hypotheses; similarities and differences between ALS/PDC and the other diseases with similar symptomologies; the relationship of ALS/PDC to other similar diseases, studies of BMAA-mediated effects in lab animals, inconsistencies and data gaps in the hypothesis; and other compounds and agents that were suggested as the cause of ALS/PDC on Guam. The review concludes that the hypothesis of a causal BMAA neurodegenerative disease relationship is not supported by existing data.