Locating the position of fixed or mobile sources (i.e., transmitters) based on measurements obtained from sensors (i.e., receivers) is an important research area that is attracting much interest. In this paper, we review several representative localization algorithms that use time of arrivals (TOAs) and time difference of arrivals (TDOAs) to achieve high signal source position estimation accuracy when a transmitter is in the line-of-sight of a receiver. Circular (TOA) and hyperbolic (TDOA) position estimation approaches both use nonlinear equations that relate the known locations of receivers and unknown locations of transmitters. Estimation of the location of transmitters using the standard nonlinear equations may not be very accurate because of receiver location errors, receiver measurement errors, and computational efficiency challenges that result in high computational burdens. Least squares and maximum likelihood based algorithms have become the most popular computational approaches to transmitter location estimation. In this paper, we summarize the computational characteristics and position estimation accuracies of various positioning algorithms. By improving methods for estimating the time-of-arrival of transmissions at receivers and transmitter location estimation algorithms, transmitter location estimation may be applied across a range of applications and technologies such as radar, sonar, the Global Positioning System, wireless sensor networks, underwater animal tracking, mobile communications, and multimedia.