Target detection is a probabilistic idea; noise and clutter prevent us from being certain to find the targets we are looking for, and will normally present us with plenty of 'targets' we are not looking for. We can only define the probabilities of detection and of false alarm that we are prepared to live with. These determine the signal-to-noise ratio that is required for detection. Optimal detection performance is achieved by maximizing the SNR at the output of the receiver. The receiver that does this uses the correlation or matched filter principle. As long as a matched filter is being used, the form of the transmitted pulse is irrelevant for detection purposes. All that matters is the ratio of the signal energy to the noise power per unit bandwidth on input to the receiver. By developing expressions for the PDFs of signal plus noise and noise only, relatively straightforward calculations of detection and false-alarm probabilities can be carried out for single pulses. These become more complicated when fluctuating targets and multiple pulses need to be considered, so that graphical or numerical techniques are needed.