Weeds are a fundamental component of agroecosystems and, if not appropriately managed, can cause severe crop yield losses. New perspectives on weed management are required, because current approaches, such as herbicide application or soil tillage, have significant environmental and agronomic drawbacks. We propose the concept of “neutral weed communities,” which are weed communities that coexist with crops and do not negatively affect crop yield and quality compared with weed-free conditions. Management practices that promote neutral weed communities can enable reduced use of herbicides and soil tillage while enhancing ecosystem services and biodiversity. We report scientific evidence of neutral weed communities and survey ecological explanations for why different weed communities have different effects on crop production. We also propose two weed management approaches for attaining neutral weed communities. The first approach aims to maximize weed biodiversity using traditional approaches such as cropping system diversification and integrated weed management. Higher weed biodiversity is associated with lower dominance of competitive weed species that reduce crop yield. The second approach relies on modern tools such as robots and biotechnology to manipulate the density of specific weed species. This approach can remove highly problematic species and minimize niche overlap between the weeds and crops. Given the complexity of interactions among crops, weeds, and other components of the agroecosystem, we highlight the need for multidisciplinary research to illuminate mechanisms that determine the neutrality of weed communities.