In the past decade, blockchain has shown a promising vision to build trust without any powerful third party in a secure, decentralized and scalable manner. However, due to the wide application and future development from cryptocurrency to the Internet of things, blockchain is an extremely complex system enabling integration with mathematics, computer science, communication and network engineering, etc. By revealing the intrinsic relationship between blockchain and communication, networking and computing from a methodological perspective, it provided a view to the challenge that engineers, experts and researchers hardly fully understand the blockchain process in a systematic view from top to bottom. In this article we first introduce how blockchain works, the research activities and challenges, and illustrate the roadmap involving the classic methodologies with typical blockchain use cases and topics. Second, in blockchain systems, how to adopt stochastic process, game theory, optimization theory, and machine learning to study the blockchain running processes and design the blockchain protocols/algorithms are discussed in details. Moreover, the advantages and limitations using these methods are also summarized as the guide of future work to be further considered. Finally, some remaining problems from technical, commercial and political views are discussed as the open issues. The main findings of this article will provide a survey from a methodological perspective to study theoretical model for blockchain fundamentals understanding, design network service for blockchain-based mechanisms and algorithms, as well as apply blockchain for the Internet of things, etc.