For the last three decades LTP has been the dominant model for studying the ways in which Hebbian learning rules are incorporated in the mammalian brain.In the process much has been learnt about the physiology and molecular biology of synaptic plasticity, but the exact relationship between LTP and learning remains elusive.In this talk I will discuss the historical background leading up to the discovery of LTp, go on to consider recent evidence which challenges the view that LTP is primarily expressed as a postsynaptic change,and conclude by asking what sorts of experiments need to be done to provide conclusive evidence that LTP provides the neural substrate for me.