A typical biosensor as shown in the figure below1
contains three main elements: a bioreceptor, a transducer, and a signal-processing element. The bioreceptor is sensitive to a particular analyte of target molecule of interest. The transducer detects that the bioreceptor has changed due to an interaction with the analyte. The signal processing elements buffers, amplifies or filters the detected signal.
There are two very good papers on biosensors in the IEEE Transactions on Nanotechnology.