Object localization in indoor areas strongly suffers from limitation of using GNSS (Global navigation satellite system ) systems due to low satellite availability and high signal attenuation. Nowadays, mobile devices such as personal computers and smart phones are emerging as a major key in today's computing platforms for indoor object localization systems due to the rapid developments in wireless communications and mobile computing. During last decade, many researchers have developed indoor localization systems through mobile devices using Wireless Fidelity (Wi-Fi) network signals with promising results and acceptable performance. In these Wi-Fi based localization systems, indoor positioning relies on different types of measurements including Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), Angle-Of-Arrival (AOA), and Received Signal Strength (RSS) of Wi-Fi signal. In this paper, the algorithms and techniques used for the RSS-based localization systems using fingerprinting method which depends on matching the recorded offline RSS from nearby access points (AP) to the online RSS received by the user on the move is reviewed. A comparison of location fingerprinting methods involving deterministic method (k-nearest neighbor method and weighted k-nearest neighbor method), probabilistic methods by estimation of likelihood functions with several approaches (non-parametric and parametric)are also explained. The performance parameters of this comparative study include the two-dimensional root mean square error (2D-rms) which measures the localization accuracy. Moreover, the effect of increasing/decreasing the number of APs on the system accuracy is also discussed. The aim of this comparison is to announce which method can provide better performance than the others and under what conditions.