Why is Cartagena such a heavily fortified city? Well, it was frequently the target of pirates of the Caribbean, who were slightly less amusing than their movie counterparts.
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Cartagena was a storage point for the gold Spaniards plundered from the indigenous people before it could be shipped to Spain, making it an attractive target for pirates. It was besieged 5 times in the 16th century alone, most notably by Francis Drake, who only stopped short of leveling the city because Spain paid him off.
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As a result, Spain decided fortresses were needed to guard the city, and you can still see these fortresses today.
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