The possible impact of algorithmic recommendation on the autonomy and free choice of Internet users is being increasingly discussed, especially in terms of the rendering of information and the structuring of interactions. This paper aims at reviewing and framing this issue along a double dichotomy. The first one addresses the discrepancy between users' intentions and actions (1) under some algorithmic influence and (2) without it. The second one distinguishes algorithmic biases on (1) prior information rearrangement and (2) posterior information arrangement. In all cases, we focus on and differentiate situations where algorithms empirically appear to expand the cognitive and social horizon of users, from those where they seem to limit that horizon. We additionally suggest that these biases may not be properly appraised without taking into account the underlying social processes which algorithms are building upon.