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Software evolves; this phenomenon causes increase in maintenance efforts, problem in comprehending the ever-changing code base and difficulty in verifying software correctness. As software changes, often the documented specification is not updated. Outdated specification adds challenge to the understanding of the code base during maintenance tasks. Also, software changes might induce bugs, anomalies and even security threats. To address the above issues, we propose an array of specification mining techniques to mine software specifications in diversified formats from program execution traces. Case studies on various systems show that the extracted specifications shed light on the behaviors of systems under analysis. Also, mined specifications can be input to existing model checkers, other formal analysis toolkits, or runtime monitors to discover bugs and anomalies.