Digital platforms and media are fertile breeding grounds for disinformation and conspirational views. They provide a variety of communication venues for a mixed set of actors and foster the diffusion of content between actor groups, across platforms and media, and across languages and geographical spaces. Understanding those diffusion processes requires approaches to measure the prevalence and spread of communicative acts within and across digital platforms. Given the increasing access to digital data, computational methods provide new possibilities to capture this spread and do justice to the interrelated nature and hybridity of online communication. Against this background, the paper focuses on the spread of conspiracy theories in digital information ecologies. It provides a review of recent methodological approaches to measuring conspiracy-related content online regarding the (a) prevalence and (b) diffusion of conspiracy theories. To that end, the paper differentiates between social network analysis approaches and computational techniques of automated text classification. It further discusses how far these and related computational approaches could facilitate studying the diffusion of conspiracy theories across different actor types, languages, topics and platforms. In doing so, it takes the specific nature of online communication and challenges in the field of conspiracy-related content into account.