This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.