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The wake generated by a moving ship may extend for many tens of kilometers in the open ocean, and can be remotely sensed. Through indirect methods, the detection of a ship and its related characteristics, is generally obtained by measuring the ship generated waves or their spectra. From the viewpoint of remote sensing, interesting problems exist related to the detection of a ship's presence and the acquisition of dynamic and static information about it. This problem can be divided into two basic aspects. First, how to obtain a moving ship's wave spectra from remotely sensed images, and second, how to extract the desired ship information from the imaged wave spectra. This thesis concentrates on the latter aspect, in particular, how to estimate a moving ship's direction, speed, length and hull shape from its wave spectra. The extraction of ship information is based on the relations of the ship's wave spectra, wave amplitude function and hull geometry. In this thesis, an analytic representation of wave elevation is introduced with the use of the Hilbert transform, and the derivation is given for the calculation of the wave amplitude function from the Fourier spectrum of one and two dimensional complex-valued wave elevations. Methods and formulas are given for estimating a ship's speed and direction from the spectrum of a two-dimensional wave patch, a single wave cut or two wave cuts. A theoretical model of the wave amplitude function is developed, and three methods are designed for the estimation of a ship's length from the wave amplitude function. Under the assumption of thin-ship theory, an inversion technique to predict the geometry of a ship's hull from the wave amplitude function or its magnitude is developed through the application of a spectral method and the constrained maximum likelihood method. Examples comparing theoretically calculated data and tow tank experimental data are given to demonstrate the methods developed and estimate performance.