  Memory effects are ubiquitous in nature and the class of memory circuit
elements - which includes memristors, memcapacitors and meminductors - shows
great potential to understand and simulate the associated fundamental physical
processes. Here, we show that such elements can also be used in electronic
schemes mimicking biologically-inspired computer architectures, performing
digital logic and arithmetic operations, and can expand the capabilities of
certain quantum computation schemes. In particular, we will discuss few
examples where the concept of memory elements is relevant to the realization of
associative memory in neuronal circuits, spike-timing-dependent plasticity of
synapses, digital and field-programmable quantum computing.
