Recently the notion of locally recoverable code (LRC) was introduced in the field of distributed storage with the goal of combating erasures. Such a code enables a recovery of any symbol of the encoding by accessing a relatively small number of other encoded symbols. In the talk, LRC codes that attain the maximum possible value of the distance for a given locality parameter and code's cardinality will be presented. These codes are based on polynomial evaluations and can be viewed as a natural generalization of Reed-Solomon codes. We will conclude with some extensions of the code construction.