Blockchain has attracted significant attention in recent years due to its potential to revolutionize various industries by providing trustlessness. To comprehensively examine blockchain systems, this article presents both a macro-level overview on the most popular blockchain systems, and a micro-level analysis on a general blockchain framework and its crucial components. The macro-level exploration provides a big picture on the endeavors made by blockchain professionals over the years to enhance the blockchain performance while the micro-level investigation details the blockchain building blocks for deep technology comprehension. More specifically, this article introduces a general modular blockchain analytic framework that decomposes a blockchain system into interacting modules and then examines the major modules to cover the essential blockchain components of network, consensus, and distributed ledger at the micro-level. The framework as well as the modular analysis jointly build a foundation for designing scalable, flexible, and application-adaptive blockchains that can meet diverse requirements. Additionally, this article explores popular technologies that can be integrated with blockchain to expand functionality and highlights major challenges. Such a study provides critical insights to overcome the obstacles in designing novel blockchain systems and facilitates the further development of blockchain as a digital infrastructure to service new applications.