The proliferation of digital communication has profoundly transformed the landscape of persuasive discourse. Online platforms have amplified the reach and impact of persuasive techniques. However, they have also enabled the rapid spread of manipulative content, targeted propaganda, and divisive rhetoric. Consequently, a wide range of computational approaches has emerged to address the multifaceted nature of digital persuasion, to detect and mitigate its harmful practices. In light of this, the paper surveys computational methods for detecting persuasive means in digital communication, focusing on how they integrate humanistic knowledge to operationalize this construct. Additionally, special emphasis is placed on models' explainability, a pivotal aspect considering these models are used by institutions to influence societal interactions. For the analysis, two primary perspectives in persuasion are defined: linguistic and argumentative. The linguistic approach analyzes specific textual features, allowing for highly accountable algorithms based on explicit rules. The argumentative approach focuses on broader persuasive mechanisms, offering greater scalability but often resulting in less explainable models due to their complexity. This tension between model sophistication and explainability presents a key challenge in developing effective and transparent persuasion detection systems. The results highlight the spectrum of methodologies for studying persuasion, ranging from analyzing stylistic elements to detecting explicitly propagandist messages. Our findings highlight two key challenges in using these algorithms to tackle societal issues of persuasion misuse: the opacity of deep learning models and the absence of a theoretically grounded distinction between vicious and virtuous persuasion. To address these challenges, we propose integrating social sciences and humanities theories to enhance the effectiveness and ethical robustness of persuasion detection systems. This interdisciplinary approach enables a more nuanced characterization of text, facilitating the differentiation between vicious and virtuous persuasion through analysis of rhetorical, argumentative, and emotional aspects. We emphasize the potential of hybrid approaches that combine rule-based methods with deep learning techniques, as these offer a promising avenue for implementing this interdisciplinary framework. The paper concludes by outlining future challenges, including the importance of multimodal and multilingual analysis, ethical considerations in handling user-generated data and the growing challenge of distinguishing between human and AI-generated persuasive content.