The location accuracy of the BeppoSAX Wide Field Cameras and acute ground- based follow-up have led to the detection of a decaying afterglow in X-rays and optical light following the classical gamma-ray burst GRB 970228. The afterglow in X-rays and optical light fades as a power law at all wavelengths. This behaviour was predicted for a relativistic blast wave that radiates its energy when it decelerates by ploughing into the surrounding medium. Because the afterglow has continued with unchanged behaviour for more than a month, its total enegy must be of order 1051 erg, placing it firmly at a redshift of order 1. Further tests of the model are discussed, some of which can be performed with available data, and implications for future observing strategies are pointed out. We discuss how the afterglow can provide a probe for the nature of the burst sources.