The vast amount of spectrum available for millimeter wave (mmWave) wireless communication systems will support accurate real-time positioning concurrent with communication signaling. This paper demonstrates that accurate estimates of the position of an unknown node can be determined using estimates of time of arrival (ToA), angle of arrival (AoA), as well as data fusion or machine learning. Real-world data at 28 GHz and 73 GHz is used to show that AoA-based localization techniques will need to be augmented with other positioning techniques. The fusion of AoA-based positioning with received power measurements for RXs in an office which has dimensions of 35 m by 65.5 m is shown to provide location accuracies ranging from 16 cm to 3.25 m, indicating promise for accurate positioning capabilities in future networks. Received signal strength intensity (RSSI) based positioning techniques that exploit the ordering of the received power can be used to determine rough estimates of user position. Prediction of received signal characteristics is done using 2-D ray tracing.