Cover crop mulch-based no-tillage (MBNT) production is emerging as an innovative alternative production practice in organic farming (OF) to reduce intensive soil tillage. Although European organic farmers are motivated to implement MBNT to improve soil fertility and achieve further management benefits (e.g., labor and costs savings), low MBNT practice is reported in Europe. Thus, this paper aims to understand the challenges of both farmers and researchers limiting the further adoption of MBNT in organic farming in temperate climates. The primary no-tillage (NT) practices of organic European farmers and findings of organic MBNT studies conducted in Europe are reviewed, focusing on living or mulch cover crop-based NT (LBNT or MBNT) for arable crop production. Major conclusions drawn from this review indicate consistent weed control and an establishment of best practices for cover crop management as the two main overarching challenges limiting adoption. In view of substantial gaps of knowledge on these issues, additional research should focus on cover crop selection and management (species, date of sowing) to increase cover crop biomass, particularly in warmer climates. Lastly, further research is needed to optimize cover crop termination to prevent competition for water and nutrients with cash crops, particularly in wetter northern conditions which promote vigorous cover crop growth.