We study the concept of type definability (a standard concept from model theory) in the context of Banach space geometry. Then we state a result which shows that there is a tight connection between type definability and asymptotic structure. Informally, the result states that in an asymptotic sense, a basic sequence (xn) in a Banach space X generates types which are definable if and only if (xn) generates almost isometric copies of `p or c0 inside X.