This paper analyses the concepts of Promise (P) and Threat (T) and their inter-relations. The objective is to study the uses of P and T in persuasion and to shed some light on related concepts such as requesting, ordering, giving prizes, punishing, etc. First, it is shown that some Ps and Ts are used for persuasion and some are conditional in nature. Using general definitions of P and T (along with the concepts of speech act and social commitment) and a broad notion of persuasion, four different typologies of P and T are introduced. They are distinguished on their conditional/non-conditional dimension and on their influencing/non-influencing aim. The focus lies on Conditional Influencing Ps and Ts (CIPs and CITs) used in persuasion. CIPs and CITs are incentive-based influencing actions rooted on dependence and power relations. Moreover, in the CIP and CIT classes the concepts of threat and promise are closely connected: the CIP is always (though often covertly) accompanied by a CIT (“if you do not do your homework I will not take you to the cinema”), and vice versa. Next, the issue is discussed of why CIPs and CITs are credible. The paper also identifies — beyond their surface, rhetorical form — a deeper difference: a ‘substantial’ threat consisting in a choice between two losses compared with a ‘substantial’ promise where the choice is between a gain and a missed-gain. It presents a pre-formal model as a basis for a computational treatment of these concepts.