Intelligent behaviour, even in humans, is an aspect of complex adaptive behaviour that provides a capacity for problem solving. This article assesses whether plants have a capacity to solve problems and, therefore, could be classified as intelligent organisms. The complex molecular network that is found in every plant cell and underpins plant behaviour is described. The problems that many plants face and that need solution are briefly outlined, and some of the kinds of behaviour used to solve these problems are discussed. A simple way of comparing plant intelligence between two genotypes is illustrated and some of the objections raised against the idea of plant intelligence are considered but discarded. It is concluded that plants exhibit the simple forms of behaviour that neuroscientists describe as basic intelligence.