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Quantum entanglement is a form of correlation between quantum particles that has now become a crucial part in quantum information and communication science. For example, it has been shown to enable or enhance quantum processing tasks such as quantum cryptography, quantum teleportation, and quantum computing. However, quantum entanglement is prone to decoherence as a result of interactions with environmental scatterers, making it an expensive resource. Therefore, it is crucial to understand its creation. We centre our attention to a situation where one would like to distribute quantum entanglement between principal particles that are apart. In this case, it is necessary to use ancillary systems that are communicated between them or interact with them continuously. Cubitt et al. showed that the ancillary systems need not be entangled with the principal particles in order to distribute entanglement. This has been demonstrated experimentally in the case of communicated ancillary particles and it is now known that the bound on the distributed entanglement is given by a communicated quantum discord. On the other hand, little is understood about the setting with continuous interactions, despite its abundant occurrence in nature. The main focus of this thesis is to study the distribution of quantum entanglement via continuous interactions with ancillary particles, which I will call mediators. I will present my work regarding the necessary conditions for entanglement distribution, the factors that are relevant for the distributed amount, and the speed limit to achieving maximum entanglement gain. Finally, I present some notable applications that can benefit from our work. This includes, among others, indirect probing of the quantum nature of optomechanical mirrors, photosynthetic organisms, and gravitational interactions.