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Multimedia contents play an important role in our society. They serve as a means of communication and can be used not only as an entertainment, but also to inform or even to disseminate knowledge. The increasing relevance of multimedia contents, such as digital images, audio, or video sequences, has been tied to the development of editing software tools enabling their adjustment and enhancement, but ultimately allowing an unskilled person to easily manipúlate them. As a consequence, their credibility as a source of information has been questioned and an important concern has arisen regarding their authenticity. With the aim of recovering trust on multimedia objects, this thesis presents new techniques to detect and localize forgeries, but likewise to infer information about the processing history undergone by a multimedia content. The design of the proposed approaches is based on the theoretical analysis of characteristic traces or footprints that emerge from the application of certain processing to multimedia contents. In this thesis the derived research work encompassing multimedia forensics is divided in two parts. The first part tackles the study of the resampling operation applied when a geometric transformation is performed to adapt a forged content to a genuine scene. The modeling of the resampling operation is addressed from different perspectives, establishing connections between this problem and other similar ones arising in distinct fields, and finally taking advantage of concepts from cyclostationarity theory, set-membership theory, or linear algebra, among others. We design different strategies for resampling factor estimation to characterize the particular transformation applied, providing estimates of the scaling factor or the rotation angle. The case of resampling detection is also considered to unveil the presence of resampling traces. The second part of the thesis is focused on the forensic analysis of video compressed sequences. We start exposing the presence of a new footprint stemming from the double compression of video streams. By exploiting this feature, the detection of double encoding and the estimation of part of the processing history of a double compressed video are further investigated. Then, being capable of extracting information from the first compression, we move to the localization of intra-frame forgeries by applying a subsequent double quantization analysis.