Nonlocality is arguably among the most counterintuitive phenomena predicted by quantum theory. In recent years, the development of an abstract theory of nonlocality has brought a much deeper understanding of the subject, revealing a rich and complex phenomenon. In the current work, we present a systematic experimental exploration of the limits of quantum nonlocality. Using a versatile and high-fidelity source of pairs of polarization-entangled photons, we explore the boundary of quantum correlations, demonstrate the counterintuitive effect of more nonlocality with less entanglement, present the most nonlocal correlations ever reported, and achieve quantum correlations requiring the use of complex qubits. All of our results are in remarkable agreement with quantum predictions, and thus represent a thorough test of quantum theory. Pursuing such an approach is nevertheless highly desirable, as any deviation may provide evidence of new physics beyond the quantum model.