Chemical interaction through airborne volatile organic compounds (VOCs) and root exudates plays a vital role in the mutualistic interactions between plants. In response to these chemical cues, a single plant can exhibit a multitude of adaption responses. Nowadays, one of the most troublesome invasive alien species (IAS) in agriculture is common ragweed ( Ambrosia artemesiifolia L.), which causes severe yield losses in various crops. Given that little is known about how chemical cues of this invader contribute to its invasiveness, we investigated the effects of airborne VOCs and root exudates released by common ragweed on growth and allocation patterns of wheat, soybean and maize, and the effects of these crops on common ragweed. Exposure to VOCs released by ragweed induced a significant reduction in the aboveground dry mass of soybean and wheat, whereas maize showed no changes in its biomass production. In contrast, ragweed itself was completely unaffected when exposed to crops or a conspecific. We observed significant changes in plant traits, such as lower biomass production, lower specific leaf area or higher chlorophyll contents after exposure to VOCs of ragweed, all of which can be linked to an increase in stress. Root choice test showed that all crops and ragweed significantly avoided root exudates of common ragweed, indicating that the root exudates as belowground cues play a vital role in ragweed and crop chemical interactions. The present study shows that the plant response to either above or below ground chemical cues is highly dependent not only on the presence but also on the identity of the neighbor pointing out the complexity of plant–plant communication.