Terror attacks have been linked in part to online extremist content. Online conversations are cloaked in religious ambiguity, with deceptive intentions, often twisted from mainstream meaning to serve a malevolent ideology. Although tens of thousands of Islamist extremism supporters consume such content, they are a small fraction relative to peaceful Muslims. The efforts to contain the ever-evolving extremism on social media platforms have remained inadequate and mostly ineffective. Divergent extremist and mainstream contexts challenge machine interpretation, with a particular threat to the precision of classification algorithms. Radicalization is a subtle long-running persuasive process that occurs over time. Our context-aware computational approach to the analysis of extremist content on Twitter breaks down this persuasion process into building blocks that acknowledge inherent ambiguity and sparsity that likely challenge both manual and automated classification. Based on prior empirical and qualitative research in social sciences, particularly political science, we model this process using a combination of three contextual dimensions -religion, ideology, and hate -each elucidating a degree of radicalization and highlighting independent features to render them computationally accessible. We utilize domain-specific knowledge resources for each of these contextual dimensions such as Qur'an for religion, the books of extremist ideologues and preachers for political ideology and a social media hate speech corpus for hate. The significant sensitivity of the Islamist extremist ideology and its local and global security implications require reliable algorithms for modelling such communications on Twitter. Our study makes three contributions to reliable analysis: (i) Development of a computational approach rooted in the contextual dimensions of religion, ideology, and hate, which reflects strategies employed by online Islamist extremist groups, (ii) An in-depth analysis of relevant tweet datasets with respect to these dimensions to