This paper proposes and experimentally implements new phase-locked loop algorithms using non-adaptive and adaptive terminal sliding modes for the three-phase grid-connected inverters. The proposed algorithms aim to extract the grid voltage phase and frequency and provide them for the inverter controller. The proposed sliding mode-based PLL algorithms provide faster, more robust, and more accurate detection of the grid voltage information compared to the conventional PI-PLL. This leads to better current controller performance and subsequently, improves the quality of the injected currents into the grid. The finite-time stability notion is incorporated with robust sliding modes to ensure a fast convergence rate. An adaptive law is proposed to determine a proper value for the switching gain which leads to a better overall performance of the PLL compared with a non-adaptive one. The Lyapunov stability theory is used to obtain the stability proofs of the closed-loop systems under both designed sliding modes-based PLLs. The proposed PLL algorithms are validated by simulation and experimental results for the three-phase grid-connected inverter under normal and various abnormal grid conditions.