All memory functions have molecular bases, namely in signal reception and transduction, and in storage and recall of information. Thus, at all levels of organisation living organisms have some kind of memory. In plants one may distinguish two types. There are linear pathways from reception of signals and propagation of effectors to a type of memory that may be described by terms such as learning, habituation or priming. There is a storage and recall memory based on a complex network of elements with a high degree of integration and feedback. The most important elements envisaged are calcium waves, epigenetic modifications of DNA and histones, and regulation of timing via a biological clock. Experiments are described that document the occurrence of the two sorts of memory and which show how they can be distinguished. A schematic model of plant memory is derived as emergent from integration of the various modules. Possessing the two forms of memory supports the fitness of plants in response to environmental stimuli and stress.