This paper presents millimeter-wave propagation measurements for urban micro-cellular and indoor office scenarios at 28 GHz and 73 GHz, and investigates the corresponding path loss using five types of path loss models, the single-frequency floating-intercept (FI) model, single-frequency close-in (CI) free space reference distance model, multi-frequency alpha-beta-gamma (ABG) model, multi-frequency CI model, and multi-frequency CI model with a frequency-weighted path loss exponent (CIF), in both line-of-sight and non-line-of-sight environments. Results show that the CI and CIF models provide good estimation and exhibit stable behavior over frequencies and distances, with a solid physical basis and less computational complexity when compared with the FI and ABG models. Furthermore, path loss in outdoor scenarios shows little dependence on frequency beyond the first meter of free space propagation, whereas path loss tends to increase with frequency in addition to the increased free space path loss in indoor environments. Therefore, the CI model is suitable for outdoor environments over multiple frequencies, while the CIF model is more appropriate for indoor modeling. This work shows that both the CI and CIF models use fewer parameters and offer more convenient closed-form expressions suitable for analysis, without compromising model accuracy when compared to current 3GPP and WINNER path loss models.