This chapter discusses the theory of optimal methods for localization of objects in pictures. One of the major goals of picture processing is to provide information on the relative location of objects in space. In many applications, detection and localization of objects is of extreme practical importance. The chapter analyzes the factors, such as signal-independent noise and the treatment of the most general situation of pictures with a cluttered background. The chapter also provides a general analysis of the potential accuracy and the reliability of object localization in the presence of additive Gaussian noise. The main problem of localization is the anomalous errors caused by the background outside objects. The problem of object localization in pictures with a complex background, like photographs of natural scenes, aerial, and space photographs of the Earth is discussed.