Plants were traditionally seen as rather passive actors in their environment, interacting with each other only in so far as they competed for the same resources. In the last 30 years, this view has been spectacularly overturned, with a wealth of evidence showing that plants actively detect and respond to their neighbours. Moreover, there is evidence that these responses depend on the identity of the neighbour, and that plants may cooperate with their kin, displaying social behaviour as complex as that observed in animals. These plant-plant interactions play a vital role in shaping natural ecosystems, and are also very important in determining agricultural productivity. However, in terms of mechanistic understanding, we have only just begun to scratch the surface, and many aspects of plant-plant interactions remain poorly understood. In this review, we aim to provide an overview of the field of plant-plant interactions, covering the communal interactions of plants with their neighbours as well as the social behaviour of plants towards their kin, and the consequences of these interactions. We particularly focus on the mechanisms that underpin neighbour detection and response, highlighting both progress and gaps in our understanding of these fascinating but previously overlooked interactions.