A bibliometric analysis, using the Scopus database as a source, was carried out in order to study the scientific documents published up to 2021 regarding the use of electrodialysis, membrane distillation, and forward osmosis for the removal of heavy metals from wastewater. A total of 362 documents that fulfilled the search criteria were found, and the results from the corresponding analysis revealed that the number of documents greatly increased after the year 2010, although the first document was published in 1956. The exponential evolution of the scientific production related to these innovative membrane technologies confirmed an increasing interest from the scientific community. The most prolific country was Denmark, which contributed 19.3% of the published documents, followed by the two main current scientific superpowers: China and the USA (with 17.4% and 7.5% contributions, respectively). Environmental Science was the most common subject (55.0% of contributions), followed by Chemical Engineering (37.3% of contributions) and Chemistry (36.5% of contribution). The prevalence of electrodialysis over the other two technologies was clear in terms of relative frequency of the keywords. An analysis of the main hot topics identified the main advantages and drawbacks of each technology, and revealed that examples of their successful implementation beyond the lab scale are still scarce. Therefore, complete techno-economic evaluation of the treatment of wastewater polluted with heavy metals via these innovative membrane technologies must be encouraged.