The increasing availability and pervasiveness of multimedia data in our society is before our very eyes. As a result of globalization and worldwide connectivity, people from all over the planet are exchanging constantly increasing amounts of images, videos, audio recordings on a daily basis. Coupled with the easy access to user-friendly editing software, this poses a number of problems related to the reliability and trustworthiness of such content, as well as its potential malevolent use. For this reason, the research field of multimedia forensics focuses on the development of forensic tools for verifying the authenticity of multimedia data. The hypothesis of pristine status of images, videos or audio tracks is called into question and can be rejected if traces of manipulation are detected with a certain degree of confidence. In this framework, studying traces left by any operation that could have been employed to process the data, either for malicious purposes or simply to improve their content or presentation, turns out to be of interest for a comprehensive forensic analysis. The goal of this doctoral study is to contribute to the field of multimedia forensics by exploiting intrinsic statistical and deterministic properties of multimedia data. With this respect, much work has been devoted to the study of JPEG compression traces in digital images, resulting in the development of several innovative approaches. Indeed, some of the main related research problems have been addressed and solution based on statistical properties of digital images have been proposed. In particular, the problem of identifying traces of JPEG compressions in images that have been decompressed and saved in uncompressed formats has been extensively studied, resulting in the design of novel statistical detectors. Given the enormous practical relevance, digital images in JPEG formats have also been considered. A novel method aimed at discriminating images compressed only once and more than once has been developed, and tested on a variety of images and forensic scenarios. Being the potential presence of intelligent counterfeiters ever increasingly studied, innovative counterforensic techniques to JPEG compression based on smart reconstruction strategies are proposed. Finally, we explore the possibility of defining and exploiting deterministic properties related to a certain processing operation in the forensic analysis. With this respect, we present a first approach targeted to the detection in one-dimensional data of a common data smoothing operation, the median filter. A peculiarity of this method is the ability of providing a deterministic response on the presence of median filtering traces in the data under investigation.