Wi-Fi technology has been thoroughly studied for indoor localization. This is mainly due to the existing infrastructure inside buildings for wireless connectivity and the uptake of mobile devices where Wi-Fi location-dependent measurements, e.g., timing and signal strength readings, are readily available to determine the user location. To enhance the accuracy of Wi-Fi solutions, a two-way ranging approach was recently introduced into the IEEE 802.11 standard for the provision of Fine Timing Measurements (FTM). Such measurements enable a more reliable estimation of the distance between FTM-capable Wi-Fi access points and user-carried devices; thus, promising to deliver meter-level location accuracy. In this work, we propose two novel solutions that leverage FTM and follow different approaches, which have not been investigated in the literature. The first solution is based on an Unscented Kalman Filter (UKF) algorithm to process FTM ranging measurements, while the second solution relies on an FTM fingerprinting method. Experimental results using real-life data collected in a typical office environment demonstrate the effectiveness of both solutions, while the FTM fingerprinting approach demonstrated 1.12m and 2.13m localization errors for the 67-th and 95-th percentiles, respectively. This is a two to three times improvement over the traditional Wi-Fi signal strength fingerprinting approach and the UKF ranging algorithm.