The approximation property originally introduced by Banach in his book in 1932 plays a fundamental role in the structure theory of Banach spaces. The first systematic study of the variants of the approximation property was initiated by Grothendieck in 1955. At that time, the main properties investigated were the approximation property (AP), the bounded approximation property (BAP), the metric approximation property (MAP) and the basis property. Trivially, a Banach space X having a Schauder basis implies X having both AP and BAP. In 1973, Enflo constructed the first famous example of a separable Banach space that fails to have the AP. Furthermore, in 1973, Figiel and Johnson constructed examples to show the connections between MAP, BAP and AP. In 1987, Szarek gave an example showing that not every Banach space with BAP has a Schauder basis. For more details on Banach space approximation properties, we refer the reader to Casszza’s comprehensive survey. Meanwhile, various approximation properties for Banach spaces are also extended and investigated to operator spaces. In summary, there has been a rich theory surrounding the approximation property of both classical and non-linear theory for Banach spaces as well as for operator spaces. Considering the nature of this investigation, it is not surprising that frame theory also plays an important role in the study of Banach space approximation properties. Combining the results of Johnson, Rosenthal and Zippin and Pełczyński in 1971, Casszza, Han and Larson introduced the Schauder frame and established the connections between Schauder frames and BAP. Later, Liu and Ruan in introduced the concept of completely bounded frames for operator spaces to obtain natural operator space analogues of corresponding Banach space results. Most recently, Liu et al. extended the Schauder frames to the Lipschitz version. This chapter is devoted to discussing some connections between frame theory and various types of Banach space approximation properties.