Recent years have seen a new form of advertisement campaigns emerge: those involving so-called social media influencers. These influencers accept money in return for promoting products via their social media feeds. Although this constitutes a new and interesting form of marketing, it also raises many questions, particularly related to transparency and regulation. For example, it can sometimes be unclear which accounts are officially influencers, or what even constitutes an influencer/advert. This is important in order to establish the integrity of influencers and to ensure compliance with advertisement regulation. We gather a large-scale Instagram dataset covering thousands of accounts advertising products, and create a categorisation based on the number of users they reach. We then provide a detailed analysis of the types of products being advertised by these accounts, their potential reach, and the engagement they receive from their followers. Based on our findings, we train machine learning models to distinguish sponsored content from non-sponsored, and identify cases where people are generating sponsored posts without officially labelling them. Our findings provide a first step towards understanding the under-studied space of online influencers that could be useful for researchers, marketers and policymakers.