This paper analyzes and constructs Locally recoverable codes. The paper initially defines Reed Solomon codes and redundant residue codes and shows the limitations of this particular encoding. The paper then defines locality and constructs Reed Solomon-like locally recoverable codes. Related to this construction is the concept of a nice polynomial and the paper provides several ways of constructing nice polynomials. The paper shows several extensions of the initial construction of locally recoverable codes. Furthermore, the paper also describes how locally recoverable can be constructed by combining several Reed Solomon codes. The paper also proves a singleton-like bound on the minimum distance and shows that almost all the locally recoverable codes constructed in this paper meet this bound with equality. Lastly, the paper defines cyclic locally recoverable codes and describes their subfield subcodes, and shows several results concerning the size of recovering sets for subfield subcodes.