  To draw a roadmap of current research activities of the blockchain community,
we first conduct a brief overview of state-of-the-art blockchain surveys
published in the recent 5 years. We found that those surveys are basically
studying the blockchain-based applications, such as blockchain-assisted
Internet of Things (IoT), business applications, security-enabled solutions,
and many other applications in diverse fields. However, we think that a
comprehensive survey towards the essentials of blockchains by exploiting the
state-of-the-art theoretical modelings, analytic models, and useful experiment
tools is still missing. To fill this gap, we perform a thorough survey by
identifying and classifying the most recent high-quality research outputs that
are closely related to the theoretical findings and essential mechanisms of
blockchain systems and networks. Several promising open issues are also
summarized finally for future research directions. We wish this survey can
serve as a useful guideline for researchers, engineers, and educators about the
cutting-edge development of blockchains in the perspectives of theories,
modelings, and tools.
