Charisma is considered as one's ability to attract and potentially influence others. Clearly, there can be considerable interest from an artificial intelligence's (AI) perspective to provide it with such skill. Beyond, a plethora of use cases opens up for computational measurement of human charisma, such as for tutoring humans in the acquisition of charisma, mediating human-to-human conversation, or identifying charismatic individuals in big social data. While charisma is a subject of research in its own right, a number of models exist that base it on various “pillars,” that is, dimensions, often following the idea that charisma is given if someone could and would help others. Examples of such pillars, therefore, include influence (could help) and affability (would help) in scientific studies, or power (could help), presence, and warmth (both would help) as a popular concept. Modeling high levels in these dimensions, i. e., high influence and high affability, or high power, presence, and warmth for charismatic AI of the future, e. g., for humanoid robots or virtual agents, seems accomplishable. Beyond, also automatic measurement appears quite feasible with the recent advances in the related fields of Affective Computing and Social Signal Processing. Here, we therefore present a brick by brick blueprint for building machines that can appear charismatic, but also analyse the charisma of others. We first approach the topic very broadly and discuss how the foundation of charisma is defined from a psychological perspective. Throughout the manuscript, the building blocks (bricks) then become more specific and provide concrete groundwork for capturing charisma through artificial intelligence (AI). Following the introduction of the concept of charisma, we switch to charisma in spoken language as an exemplary modality that is essential for human-human and human-computer conversations. The computational perspective then deals with the recognition and generation of charismatic behavior by AI. This includes an overview of the state of play in the field and the aforementioned blueprint. We then list exemplary use cases of computational charismatic skills. The building blocks of application domains and ethics conclude the article.