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One in a series of talks from the 2019 Models of Consciousness conference. Anita Mehta Leverhulme Visiting Professor, University of Oxford Short- and long-term memories are distinguished by their forgettability. Most of what we perceive and store is lost rather quickly to noise, as new sensations replace older ones, while some memories last for as long as we live. Synaptic dynamics is key to the process of memory storage; in this talk I will discuss a few approaches we have taken to this problem, culminating in a model of synaptic networks containing both cooperative and competitive dynamics. It turns out that the competition between synapses is key to the natural emergence of long-term memory in this model, as in reality. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.