Given the central role that online platforms (OPs) play in the digital economy, questions arise about their responsibility in relation to illegal/harmful content or products hosted in the frame of their operation. Against this background, this study reviews the main legal/regulatory challenges associated with OP operations and analyses the incentives for OPs, their users and third parties to detect and remove illegal/harmful and dangerous material, content and/or products. To create a functional classification which can be used for regulatory purposes, it discusses the notion of OPs and attempts to categorise them under multiple criteria. The study then maps and critically assesses the whole range of OP liabilities, taking hard and soft law, self-regulation and national legislation into consideration, whenever relevant. Finally, the study puts forward policy options for an efficient EU liability regime: (i) maintaining the status quo; (ii) awareness-raising and media literacy; (iii)promoting self-regulation; (iv) establishing co-regulation mechanisms and tools; (v) adoptingstatutory legislation; (vi) modifying OPs' secondaryliability by employing two different models – (a) byclarifying the conditions for liability exemptionsprovided by the e-Commerce Directive or (b) byestablishing a harmonised regime of liability.