Most people consider cockroaches to be quintessential urban pests, even though very few of the 5000 cockroach species live in urban areas. The German cockroach is the most widespread and common cockroach in urban areas, however how this invasive species has spread globally is poorly understood. We reviewed the published and grey literatures, and museum data, to document the spread of the German cockroach, and how it may have interacted with other urban cockroach species. We found that the German cockroach likely originated from South Asia, was introduced into Europe no later than the 18th century, from where it invaded worldwide. The spread of the German cockroach was facilitated by the improvement of transportation technologies, especially from colonial trading, and indoor heating in cooler climates. Studies of population genetics have found that once introduced into a new location, the German cockroach spread rapidly through local expansion, and this could be within single (large, multiple-story) buildings. This local expansion resulted in displacement of other urban cockroach species, likely due to their small size requiring fewer resources, shorter generation times and so faster evolution, especially for pesticide resistance. These findings may help to identify new pest management methods. Future research could use genetic tools at larger scales to map distribution routes across the globe and interaction with pesticides and the evolution of resistance.