The interrelated logical concepts of validity, entailment, and consequence are all standardly defined in terms of truth preservation. However, imperative sentences can stand in these relations, but they are not truth-apt (they do not express propositions). This puzzle can be understood as an inconsistent triad: T1 Imperatives can be the relata of the consequence relation. T2 Imperatives are not truth-apt. T3 The relata of the consequence relation must be truth-apt. These three claims cannot all be true. So, to solve the problem of imperative consequence we must reject one of the three claims. Solutions can be categorised into three types: those that reject T1, those that reject T2, and those that reject T3. In this thesis, I first outline and motivate each of these three claims. I then consider, in turn, theories of imperative logic and semantics, all of which fall into one of the three types of solution. I consider and reject two versions of solution type 1, the type that rejects T1. These versions argue that it is impossible for imperatives to stand in logical relations, and attempt to provide alternative explanations for what's happening when it seems like they are doing so. I then consider and reject several versions of solution type 2, the type that rejects T2. These theories claim that, despite appearances based on surface grammar, imperatives are disguised declaratives and thus truth-apt. Each theory proposes a translation schema – it outlines the truth-conditions for imperatives. Next, I outline several versions of solution type 3, the type that rejects T3. These theories aim to develop a formal account of imperative logic. I reject each of these theories in turn, and finally propose a solution that avoids the problems I raise with the other theories.