A renewed understanding of eco-friendly principles is moving the industrial sector toward a shift in the utilization of less harmful solvents as a main strategy to improve manufacturing. Green analytical chemistry (GAC) has definitely paved the way for this transition by presenting green solvents to a larger audience. Among the most promising, surely DESs (deep eutectic solvents), NaDESs (natural deep eutectic solvents), HDESs (hydrophobic deep eutectic solvents), and HNaDESs (hydrophobic natural deep eutectic solvents), with their unique features, manifest a wide-range of applications, including their use as a means for the extraction of small bioactive compounds. In examining recent advancements, in this review, we want to focus our attention on some of the most interesting and novel ‘solvent-free‘ extraction techniques, such as microwave-assisted extraction (MAE) and ultrasound-assisted extraction (UAE) in relation to the possibility of better exploiting DESs and NaDESs as plausible extracting solvents of the phenolic compounds (PCs) present in different matrices from olive oil components, such as virgin olive pomace, olive leaves and twigs, virgin and extra virgin olive oil (VOO and EVOO, respectively), and olive cake and olive mill wastewaters (OMWW). Therefore, the status of DESs and NaDESs is shown in terms of their nature, efficacy and selectivity in the extraction of bioactive phytochemicals such as secoiridoids, lignans, phenolic acids and alcohols. Related studies on experimental design and processes’ optimization of the most promising DESs/NaDESs are also reviewed. In this framework, an extensive list of relevant works found in the literature is described to consider DESs/NaDESs as a suitable alternative to petrochemicals in cosmetics, pharmaceutical, or food applications.