In the past decade, blockchains have emerged as a new class of decentralized systems and are regularly viewed as disruptive technology with many applications. For security research, blockchains are of particular interest because they operate in a radically new, highly adversarial environment where protocol flaws and software bugs can be immediately monetized by anonymous actors. This dissertation focuses on the complexity of designing protocols that are secure in this new adversarial environment. In the process, it questions established modeling assumptions in well-studied, longstanding security frameworks, and finds novel insights about classical security notions. It aims to highlight how the blockchain environment provides a guiding principle for how we should think about the robustness of our systems more broadly. The first part of this dissertation shows how a prominent blockchain application, decentralized finance, surfaces an under-specification in the well-studied consensus primitive from distributed systems research. The second part shows how new capabilities like trusted hardware, multi-party computation, and smart contracts, which are typically used for building secure systems, can also be employed by attackers for nefarious purposes. This results in powerful new attacks that surface subtle gaps in existing literature on proofs of knowledge and accountability in cryptography. The work in this dissertation benefits from techniques rooted in several areas---distributed systems, cryptography, mechanism design and game theory, and social choice. The hope is that this further motivates an intersectional lens for blockchain (and more generally, modern systems) security.