Does the cryptocurrency market evolve? This dissertation focuses on the market properties and relevant policies of cryptocurrency, which has emerged and sparked the attention of academia and policymakers over the last decade. Applying the complex system theory and quantum dynamics, the empirical analysis exhibits a portrait of the cryptocurrency market that shows financial and economic characteristics not far from the other classical assets. The first study suggests that the Bitcoin market is not significantly different in terms of long-run market equilibrium, even though it is less efficient than that of the others. A theoretical explanation is provided by the power law and Laplace distribution function derived from the solution of Fokker-Planck equation. The second study investigates the technological split of blockchain, i.e., the “hard fork” phenomenon, and reveals an asymmetric information flow from Bitcoin to its derivative coin market. The third study finds that the Bitcoin market is close to being efficient, using the quantum harmonic oscillator model. In particular, overlapping eigenfunctions quantized on the Hilbert space simultaneously capture both Gaussian and non-Gaussian states of the Bitcoin market. Lastly, a discussion is also offered about the policy implications and the development of the cryptocurrency market in the future.