Blockchain systems are global-scale peer-to-peer systems that integrate many techniques and protocols from cryptography, distributed systems, and databases. In a blockchain system, nodes agree on their shared states across a large decentralized network of possibly untrusted participants. Bitcoin and other cryptocurrencies are permissionless blockchain systems. In permissionless blockchain systems, computing nodes without a priori known identities can join or leave the blockchain network at any time. On the other hand, a permissioned blockchain system uses a network of a priori known and identified nodes to manage the blockchain. While the focus of this monograph is on permissioned blockchains, in this chapter, we present preliminary concepts and techniques used in both permissionless and permissioned blockchains.