Compared with conventional measurements from supervisory control and data acquisition (SCADA) system, phasor measurement units (PMUs) provide time-synchronized and direct measurements of phasors. The availability of synchronized phasor measurements can significantly improve power system protection and analysis. This dissertation is specifically committed to using synchronized measurements for estimation of fault locations in transmission systems. Transmission lines are prone to various short-circuit faults. Accurate fault location is critical for rapid power recovery. Chapter 2 proposes a new fault location method based on sparse wide area measurements. One distinguishing feature of this method is its applicability to both transposed and untransposed transmission lines. In addition, the method is developed based on sparse-wide area measurement that may be taken far away from the faulted line. Shunt capacitances of transmission lines are also fully considered by the algorithm. Moreover, when synchronized measurements from multiple buses are available, an optimal estimator can be used to make the most use of measurements, and to detect and identify potential bad measurements. Most of the existing fault location literatures discuss common shunt faults, including single line-to-ground faults, line-to-line faults, line-to-line-to-ground faults, and three-phase faults. However, in addition to common shunt faults, some complex faults may also occur in power systems. Among these complex faults, evolving fault and inter-circuit fault are two typical examples. Chapter 3 extends the method developed in Chapter 2 to deal with evolving faults. The proposed wide-area fault location methods are immune to fault type evolution, and are applicable to both transposed and untransposed lines. Chapter 4 discusses location of inter-circuit faults. Inter-circuit fault is a type of simultaneous fault, and it is the most common simultaneous fault type. Inter-circuit faults between each circuit in a double-circuit line is the most common inter-circuit fault. A fault location method for inter-circuit faults on double-circuit lines are developed and evaluated in Chapter 4. Chapter 5 puts forward a fault location algorithm, which does not require line parameters information, for series-compensated transmission lines. Two-end synchronized voltage and current measurements are utilized. The proposed method is independent of source impedance and fully considers shunt capacitances of transmission lines.