The polarization observed in digital spaces makes them a prototypical playground for the study of sets of actors cohesively connected to alters holding similar opinions. Such socio-semantic bubbles raise the issue of resilience at two levels, whereby macro-level resilience may conflict with meso-level resilience: put differently, the deliberative capacity of a social system may be disrupted by the stability of groups whose members hardly encounter diverging narratives. This chapter reviews our current knowledge on the empirical socio-semantic cohesiveness of bubbles and on the normative models explaining their plausible emergence. It also aims at challenging the common correspondence between low-level homophily and high-level fragmentation, that neither holds nor suffices to explain the wide spectrum of socio-semantic configurations observed across a myriad of online systems. It proposes further research directions in this regard, while reviewing the ongoing efforts for understanding the potential role of algorithms in the emergence of online socio-semantic bubbles.