In this paper, we briefly review the concept of memory circuit elements, namely memristors, memcapacitors and meminductors, and then discuss some applications by focusing mainly on the first class. We present several examples, their modeling and applications ranging from analog programming to biological systems. Since the phenomena associated with memory are ubiquitous at the nanoscale, we expect the interest in these circuit elements to increase in coming years. ; Comment: to be published in the Journal of Computational and Theoretical Nanoscience