Embedded software is developed under the assumption that hardware execution is always correct. Fault attacks break and exploit that assumption. Through the careful introduction of targeted faults, an adversary modifies the control-flow or data-flow integrity of software. The modified program execution is then analyzed and used as a source of information leakage, or as a mechanism for privilege escalation. Due to the increasing complexity of modern embedded systems, and due to the difficulty of guaranteeing correct hardware execution even under a weak adversary, fault attacks are a growing threat. For example, the assumption that an adversary has to be close to the physical execution of software, in order to inject an exploitable fault into hardware, has repeatedly been shown to be incorrect. This article is a review on hardware-based fault attacks on software, with emphasis on the context of embedded systems. We present a detailed discussion of the anatomy of a fault attack, and we make a review of fault attack evaluation techniques. The paper emphasizes the perspective from the attacker, rather than the perspective of countermeasure development. However, we emphasize that improvements to countermeasures often build on insight into the attacks.