Our work deals with the detection and localization of acoustic sources in shallow underwater channels. These are signal processing problems of paramount importance in many underwater acoustic applications. The performance of these applications is limited by the high ambient noise in the ocean which is often non-Gaussian. Moreover, the signal field measured at a sensor array, due to an acoustic source in shallow ocean, is generally unknown. We focus on algorithms that employ acoustic vector sensors (AVS), a new type of sensors that are superior to the conventional pressure sensors. This allows the development of improved algorithms without a need for increase in the size of the sensor array to be deployed in the shallow ocean. The problem of detection is dealt with in three parts – (i) detection using an array of AVS in Gaussian noise, (ii) detection using a single sensor in non-Gaussian noise and (iii) detection using an array of AVS in non-Gaussian noise. In a shallow-ocean detection scenario, implementation of the optimal detector requires complete knowledge of the signal field at the array and is hence impractical. Using generalized likelihood ratio testing, we design suboptimal detectors that utilize partial knowledge of the signal field for such a case. We first formulate these detectors for the simpler case of Gaussian environmental noise and then extend this to the more general and practical case of non-Gaussian noise. We explore how detection performance in non-Gaussian noise can be enhanced by using an SSR preprocessor and show that this provides a simple and near-optimal solution to detection in a wide range of non-Gaussian noise pdfs. Source localization algorithms in an ocean environment are severely affected by low SNR and perform poorly because they do not exploit the known fact that the environmental noise is non-Gaussian in nature. We present a method to improve the performance of azimuth estimation algorithms by combining the SSR phenomenon with conventional azimuth estimation methods. This offers better performance with relatively no increase in complexity. We also develop a MUSIC-based approach for three-dimensional localization of a single source in the near-field using a single AVS. This method yields closed-form expressions for the location estimates thus allowing 3D source localization with low computational complexity.