How did the "wise men" become known as 3 kings?

In Matt 2, the men from east who came to visit Baby Jesus are referred to as wise men. However, now they are also known as three kings. When did they become known as "kings" rather than "wise men" and what is the basis for the description? Additionally, they are often referred to as the 3 magi. What is the basis for each of these descriptors?