No megathrust earthquake similar to the Magnitude class 9 events in Sumatra in 2004 or in Japan in 2011 was firmly reported at the Lesser Antilles subduction zone. The largest known tsunamis followed either a strong intraplate earthquake (1867, Virgin Islands) or were transoceanic due to the 1755 Lisbon earthquake. In this region, where the convergence rate between the American and Caribbean plate is low, the recurrence time of large earthquakes may be long (several centuries or millennia) and the historical record of such events is short. It is thus difficult to estimate their impact and becomes crucial to gain information from longer-term geological records and tsunami modeling. An increasing number of old prehistoric tsunami deposits have been identified in recent years on several islands in the northern segment of the Lesser Antilles arc, between Antigua and Puerto-Rico, in Anegada, St-Thomas (Virgin Islands), Anguilla and Scrub islands. Here, we carefully review all those studies and evidenced that most tsunami deposits are about 500 to 800 years old (1200 to 1500 cal yrs. CE) likely suggesting a large event or a cluster of events at that time. We combined information provided by the sedimentological records (distribution and altitude of the sediment deposits) and tsunami models to discuss the origin of the middle age Pre-Colombian event(s). We listed all faults as possible sources of tsunamis in this complex tectonic region. We performed 35 run-up models by using high-resolution/topographic grids to compare the simulated wave heights and run-up distance to the sediment record. We showed that few models are able to generate tsunami waves which heights and run-up distances match the characteristic of the observed tsunami deposits. These models are Magnitude class 9 M-thrust earthquakes rupturing the subduction interface between 30 km in depth to the trench facing Anegada Island. Magnitude class 8 outer-rise earthquakes, modeled along the trench, are other candidates for the Pre-Columbian event(s) although less convincing than the mega-thrust ones. The realism of these models is discussed in the light of the recent coupling models of the subduction zone based on short-term geodetic records. Finally, considering all the results and data, the equally strong hypothesis that these sediments were deposited by one or several storms remains less convincing than our tsunamigenic earthquakes scenarios. We conclude that the occurrence of one or several large megathrust or outer-rise earthquakes in association with damaging tsunamis likely have occurred in the past in the Lesser Antilles and could occur again in the future. This opens the discussion on the threat posed by such catastrophic event in these densely populated and touristic regions.