Arithmetic of elliptic curves through the ages

This expository article is based on a talk that was given at the EWM Symposium held at Cambridge, U.K., in October 2007. The talk was aimed at a broad and general audience and I have tried to retain the flavour of the original lecture while converting it to its present text version. I have also attempted to make the bibliography as comprehensive as possible, but given the vastness of the subject, apologise for any inadvertent omissions. I would like to thank the organisers of the EWM conference for the invitation to speak, and John Coates for helpful discussions and comments. It is a pleasure to thank Chennai Mathematical Institute for hospitality accorded both at the time of preparing the talk, and later, while writing the article.