Algorithms, indispensable to understand Artificial Intelligence (AI), are omnipresent in social media but users’ understanding of these computational processes and the way they impact their consumption of information is often limited. There is a need for Media and Information Literacy (MIL) research investigating a) how MIL can support Algorithm Literacy (AL) as a subset of competences, and with what working definition, b) what competences users need in order to evaluate algorithms critically and interact with them effectively, and c) how to design learner-centred interventions that foster increased user understanding of algorithms and better response to disinformation spread by such processes. Based on Crossover project research, this paper looks at four scenarios of use by journalists, developers and MIL experts that mirror users’ daily interactions with social media. The results suggest several steps towards integrating AL within MIL goals, while providing a concrete definition of Algorithm-literacy that is experience-based. The competences and design considerations are organised in a conceptual framework thematically derived from the experimentation. This contribution can support AI developers and MIL educators in their co-design of algorithm-literacy interventions and guide future research on AL as part of a set of nested AI literacies within MIL.