The low radiation dose rates used in nuclear medicine necessitate image formation and measurements that are severely count limited. This limitation may mask our ability to perceive contrast in an image or may affect our confidence in quantitative functional measurements. The randomness of the signal can be described by using the Poisson probability distribution with its associated mean and variance. The validity of a measurement and uncertainties in a result can be determined by examining the count statistics. If multiple measurements are used to derive a result, confidence levels can be determined by examination of the propagation of errors. The statistical properties of the detected signal can also be evaluated to determine if the equipment is functioning properly. For example, the chi2 test can be used to determine if there is too much or too little variability in count samples. Finally, image formation with limited numbers of photons results in noisy images that may be difficult to interpret. An understanding of the trade-offs between contrast, noise, and object size is required to set proper image acquisition parameters and thereby ensure that the information required to make a diagnosis is contained in the final image.