This tutorial studies relationships between differential privacy and various information-theoretic measures by using several selective articles. In particular, we present how these connections can provide new interpretations for the privacy guarantee in systems that deploy differential privacy in an information-theoretic framework. To this end, the tutorial provides an extensive summary on the existing literature that makes use of information-theoretic measures and tools such as mutual information, min-entropy, Kullback-Leibler divergence and rate-distortion function for quantification and characterization of differential privacy in various settings.