Beyond direct synaptic communication, neurons are able to talk to each other without making synapses. They are able to send chemical messages by means of diffusion to target cells via the extracellular space, provided that the target neurons are equipped with high-affinity receptors. While synaptic transmission is responsible for the 'what' of brain function, the 'how' of brain function (mood, attention, level of arousal, general excitability, etc.) is mainly controlled non-synaptically using the extracellular space as communication channel. It is principally the 'how' that can be modulated by medicine. In this paper, we discuss different forms of non-synaptic transmission, localized spillover of synaptic transmitters, local presynaptic modulation and tonic influence of ambient transmitter levels on the activity of vast neuronal populations. We consider different aspects of non-synaptic transmission, such as synaptic-extrasynaptic receptor trafficking, neuron-glia communication and retrograde signalling. We review structural and functional aspects of non-synaptic transmission, including (i) anatomical arrangement of non-synaptic release sites, receptors and transporters, (ii) intravesicular, intra- and extracellular concentrations of neurotransmitters, as well as the spatiotemporal pattern of transmitter diffusion. We propose that an effective general strategy for efficient pharmacological intervention could include the identification of specific non-synaptic targets and the subsequent development of selective pharmacological tools to influence them.