The ever-increasing advances in quantum information technology represent a disruptive force in the realm of information security. A prime example is quantum key distribution (QKD), which has reached a level of maturity such that commercial products are available and used, e.g. in banks, and the first quantum communication satellite is already in orbit.There exists a wide gap between classical and quantum cryptography, and over the past three decades, research in the field of quantum cryptography has produced a wide range of cryptographic primitives and algorithms that have been shown to be either impossible to achieve using classical means or to be inherently superior to their classical counterparts. On the other hand, important classical concepts have been shown to be impossible in quantum information processing.Surprisingly, the fundamental notion of deniability has been largely ignored by the quantum information processing community. Deniability can be seen as another aspect of privacy, which is of central importance in various scenarios such as off-the-record communication, anonymous reporting and coercion-resistant secure electronic voting. One form of deniability can be defined as the ability for the sender of a message to deny, e.g. in court, the actual content of the message.The goal of this project is to conduct a thorough formal analysis of the promising, but poorly understood field of deniable quantum communication. This will contribute to the body of knowledge on possibility and impossibility results for quantum communication, which will not only be relevant for the future development of this field in both a cryptographic and commercial sense, but also for governments and law makers deciding on the use of such technologies.To be precise, we will first conduct an exhaustive survey on existing solutions for deniability in the classical literature, along with a systematic analysis and classification of the quantum primitives that are relevant for deniability. Then we will create a formal and rigorous adversarial and computational model that will capture the different real-world threat models, and give precise definitions of deniability and related concepts in quantum protocols. This systematic approach enables us to explore and better understand the extent to which various forms of deniability can be achieved under well-defined constraints. The results will be both in the form of impossibility, as well as feasibility theorems. In the latter case, actual protocols satisfying deniability will be developed. This will be both in the form of modifying existing QKD protocols to restore deniability, as well as devising new quantum protocols that provide deniability for key exchange and beyond, e.g. for e-voting. The methodology will be continuously supported by software prototyping aimed at running simulations and validating our approach and results.