If biology throughout the nineteenth and twentieth centuries was dominated by the metaphor of the machine, the metaphor underlying twenty first century biology is that of the network or web. A rapid proliferation of molecular data coupled with increased computational power has revealed that gene regulation, protein interaction, the topology of metabolism and signal-transduction in and between cells, tissues, organs and organisms can all be described as robust, resilient and modular networks. Such small-world networks are characterised by rapid signal propagation, a capacity for computation and for synchronisation between the same, or different, hierarchic levels. Organelles, cells, tissues, organisms and ecosystems are not mere aggregations of components, but are hierarchies of interacting systems or modules, each possessing a degree of autonomy, and each a degree of interdependence. Into this metaphor of the network has emerged the discipline of integrative plant electrophysiology, called by its adherents, plant neurobiology. This field aims to understand how plants perceive, recall and process experience, coordinating behavioural responses via integrated information networks that include molecular, chemical and electrical levels of signalling. Integrative plant electrophysiology rejects the long standing view of plants as passive insensate automata that react to the environment with mechanical simplicity. The controversial use of the word ‘neurobiology’ as applied to plants signifies that long-distance electrical signals, such as action potentials, convey meaningful information from the site of initiation to a distant site, where the signal is interpreted and evaluated, and an adaptive behavioural response is mounted. Such inter-module communication is ‘nervous’ in the sense that it is adaptive, thereby implying capacities for memory, learning, anticipating the future and for generating novel responses. By itself a touch stimulus is meaningless, and by itself a behaviour (e.g. Mimosa leaf folding) is meaningless. Meaning lies in the network of processes that associate and integrate these events. Communication processes within, and between plants and associated organisms, can therefore be considered as biosemiotic, involving as they do the interpretation and evaluation of stimuli. This review traces historical aspects of the development of integrative plant electrophysiology and the methods that inform it, with a special emphasis on the work of Indian biophysicist Sir J. C. Bose (1858–1937), who, in an impressive body of published research, proposed that plants and animals share essentially similar fundamental physiological mechanisms. The first scientist to appreciate that responses in plants (e.g. leaf folding in the sensitive plant Mimosa) constitute behaviour reliant on integrative electrical signals; Bose argued further that all plants co-ordinate their movements and integrate their responses to the world through electrical signalling. Despite their sessile habits, plants are to be regarded as sensate, active, intelligent explorers of the world. Bose identified a fundamental physiological motif that interlinked measurable pulsations or oscillations in cellular electric potentials with oscillations in cell turgor pressure, cellular contractility and growth. All plants respond to the world and to other living things through adaptations of this pulsatile motif, an electromechanical pulse that underlies electro-osmotically enacted behaviour. J.C. Bose’s conclusions that all plants possess a nervous system, a form of intelligence, and a capacity for remembering and learning, were poorly received by prominent electrophysiologists of his time. Experiments devoted to plant responsiveness, inter-organism communication, kin-recognition, foraging, intelligence and learning as mediated by electrical signalling, are now published and debated in the mainstream literature as aspects of integrative plant electrophysiology.