The research in the sixth generation of communication networks needs to tackle new challenges in order to meet the requirements of emerging applications in terms of high data rate, low latency, high reliability, and massive connectivity. To this end, the entire communication chain needs to be optimized, including the channel and the surrounding environment, as it is no longer sufficient to control the transmitter and/or the receiver only. Investigating large intelligent surfaces, ultra massive multiple-input multiple-output, and smart constructive environments will contribute to this direction. In addition, to allow the exchange of high dimensional sensing data between connected intelligent devices, semantic and goal oriented communications need to be considered for a more efficient and context-aware information encoding. In particular, for multi-agent systems, where agents are collaborating together to achieve a complex task, emergent communications, instead of hard coded communications, can be learned for more efficient task execution and communication resources use. Moreover, new physics phenomenon should be exploited such as the thermodynamics of communication as well as the the interaction between information theory and electromagnetism to better understand the physical limitations of different technologies, e.g, holographic communications. Another new communication paradigm is to consider the end-to-end approach instead of block-by-block optimization, which requires exploiting machine learning theory, non-linear signal processing theory, and non-coherent communications theory. Within this context, we identify twelve scientific challenges for rebuilding the theoretical foundations of communications, and we overview each of the challenges while providing research opportunities and open questions for the research community.