This article proposes an analytical approach to algorithms that stresses operations of folding. The aim of this approach is to broaden the common analytical focus on algorithms as biased and opaque black boxes, and to instead highlight the many relations that algorithms are interwoven with. Our proposed approach thus highlights how algorithms fold heterogeneous things: data, methods and objects with multiple ethical and political effects. We exemplify the utility of our approach by proposing three specific operations of folding-proximation, universalisation and normalisation. The article develops these three operations through four empirical vignettes, drawn from different settings that deal with algorithms in relation to AIDS, Zika and stock markets. In proposing this analytical approach, we wish to highlight the many different attachments and relations that algorithms enfold. The approach thus aims to produce accounts that highlight how algorithms dynamically combine and reconfigure different social and material heterogeneities as well as the ethical, normative and political consequences of these reconfigurations.