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Quantum resource theories allow us to quantify a useful quantum phenomenon,to develop new protocols for its detection and determine the exact processesthat maximize its use for practical tasks. These theories aim at transformingphysical phenomena, such as entanglement and quantum coherence, into usefulproperties for the execution of concrete tasks related to quantum information.In this thesis, we focus on the resource theories of entanglement, discord-likequantum correlations, and quantum coherence, the most intriguing quantumphenomena exploited so far in quantum information theory. We begin bypresenting in detail the theoretical tools of these quantum resources, focusingon the most remarkable techniques and computational problems. In this sense, wediscuss several mathematical methods that solve some problems related to theirquantifications, and some analytical results for bipartite quantum systems aregiven. We also examine the intrinsic connections between these quantumresources by extracting the links that unite the corresponding measures. Incontrast, the revolution of quantum technology has led to a growing interest inquantum metrology, and quantum entanglement has been employed to overcome theclassical limit in several quantum estimation protocols. In this work, weanalyze the role of quantum correlations beyond entanglement in improving theaccuracy of an unknown parameter. According to our results, correlations can becaptured using quantum Fisher information, and quantum discord correlations canbe exploited to ensure the accuracy of phase estimation protocols. This thesisincludes also the contributions on the dynamics of these quantum resources invarious models of open quantum systems. Among our objectives, is to study theeffects of the environment on these quantum resources and to obtain techniquesto protect them from the effects of intrinsic decoherence.

Intrinsic relationships of Quantum Resource Theories and their roles in Quantum Metrology