This article introduces several contributions to enhance an important application such as acoustic tomography (AT), using mainly the spatial and spectral diversities of underwater acoustic signals. Due to their inherited properties, (i.e. spareness, non-stationarity or cyclostationarity, wide-band frequency range, wide range of power, etc.), the process of underwater acoustic signals becomes a real challenge for many scientists and engineers who are involved in studies related to the ocean. For various applications, these studies require huge and daily information. AT techniques remain fast and cheap ways to obtain such data. Nowadays, active acoustic tomography (AAT), is communally used to generate powerful and repetitive acoustic sources. Recently, researchers have been attracted by an alternative way, called passive acoustic tomography (PAT), which uses acoustic opportune signals of their environment. PAT techniques are mainly used for ecological, economical and other reasons such as military applications. With PAT, no signal is emitted; therefore, problems become more challenging. The number and positions of existent sources are unknown, and sensors measure mixtures of available sources. Algorithms based on time or frequency domains are widely deployed to classify, identify, and study received signals in AAT applications. For PAT, researchers employ multiple sensors in order to add an extra dimension, (such as space). This article focuses on approaches used in space along with time or frequency to extract information, improve performances, and simplify the overall architecture. This article explains the use of signal processing and statistical approaches to solve problems raised using PAT and discusses the experimental results. The review of the literature offers a big variety of algorithms to deal with classic AAT problems. Therefore, only problems related to PAT have been considered herein.