Axiom gives smart contracts trustless access to the entire history of Ethereum and arbitrary ZK-verified compute over it. Developers can send on-chain queries into Axiom, which are trustlessly fulfilled with ZK-verified results sent in a callback to the developer's smart contract. This allows developers to build rich on-chain applications without additional trust assumptions. Axiom builds a brief mental model of zkSNARKs and give an overview of application design patterns and techniques for ZK-enabled apps. We focus on the overall landscape of proving environments and applications of each: the affordances of browser proving, mobile proving, server proving, GPU proving, etc.