In the present study, advanced extraction techniques, microwave (MAE), ultrasound (UAE), and high pressure (HPAE)-assisted extraction, were applied to improve extraction efficiency of olive (Olea europaea L.) leaves polyphenols. The effect of sample mass (1.5 and 3 g), MAE—time (2, 8.5, and 15 min) and temperature (45 and 80 °C), UAE—time (7, 14, and 21 min) and amplitude (50 and 100%) and HPAE—time (1, 5.5, and 10 min) and pressure (300 and 500 MPa) on the concentration of each analyzed polyphenol compound was examined. Identified polyphenols were oleuropein, hydroxytyrosol, chlorogenic acid, caffeic acid, verbascoside, and rutin. All three advanced extraction techniques yielded higher content of total polyphenols when compared to the conventional heat-reflux extraction (CE) along with a significant reduction of extraction time from 60 (CE) to 2, 21, and 5.5 min in MAE, UAE, and HPAE, respectively. The most intensive values of tested parameters in each technique were the ones that promoted cell wall disruption, e.g., temperature of 80 °C in MAE, 100% amplitude in UAE and 500 MPa in HPAE. MAE and UAE were more efficient in total polyphenols’ recovery than HPAE.