Exploring network path properties is useful not only for both consumers and providers to verify service level agreement, choose the best route, and diagnose performance problems; but also for network applications and services to adapt to network path characteristics and improve their performance. However, the design and implementation of a reliable measurement method is very challenging for the Internet landscape today. It is difficult to obtain accurate measurement in the midst of interference from cross traffic which can intervene measurement traffic and cause packet loss. Another challenge is to characterize asymmetric-path (i.e., forward and reverse paths) properties between a measuring node and a remote endpoint, where acquiring the remote endpoint's cooperation (in terms of setting up additional software) is usually impracticable. Although many methods can seamlessly perform non-cooperative measurement, most of them measure either round-trip path properties or restricted configurations of asymmetric paths. In this research, we first propose a fast and efficient method, called minimum delay difference (MDDIF), for path capacity measurement using packet pairs. The path capacity is defined as the smallest transmission rate of a set of links forming a network path. Measuring the path capacity is difficult, because the accuracy and speed can be adversely affected by cross traffic present on the path. Moreover, minimizing the amount of overheads, including the amount of measurement traffic and the storage and computation requirement, are also important to make the measurement feasible for a practical network. Unlike the classic methods based on packet-pair dispersion filtering, the MDDIF method only requires a minimal possible delay for the first packet and a minimal possible delay for the second packet, where the two delays generally come from different packet pairs. Our proofs and first-passage-time analysis show that the MDDIF method is correct and that it takes less time to obtain accurate samples than the minimum delay sum (MDSUM) method. We have incorporated the MDDIF method into HTTP/OneProbe, a noncooperative probing method based on TCP data probes and HTTP/1.1, and conducted extensive testbed and Internet experiments to evaluate the MDDIF method. While most attention and effort have been put on the path capacity measurement for one-way or round-trip network paths, the development of robust methods for measuring capacity asymmetry is still in its infancy. As the second main contribution, we propose TRIO, a noncooperative method for measuring capacity asymmetry. By using three minimum round-trip times (minRTTs), TRIO can measure both forward-path capacity and reverse-path capacity at the same time. Since TRIO does not measure packet dispersion directly, it removes the packet size limitation and therefore can measure any degree of capacity asymmetry. TRIO also mitigates the cross-traffic interference using the minRTT information and a round-trip capacity estimate. Both analytical models and empirical evaluation conducted in a testbed and the Internet report accurate measurement results obtained by TRIO. One of the fundamental effects of cross traffic is network congestion at routers that will cause packet loss and defeat the measurement of various network path properties (e.g., round-trip delay and path capacity). Notwithstanding this adverse impact, on the bright side, cross traffic can help the formation of loss pairs, which was proposed a decade ago, for discovering other network path properties such as a router's buffer size. A packet pair is regarded as a loss pair if exactly one packet is lost. Therefore, the residual packet's delay could be used to infer the lost packet's delay. Despite this unique advantage shared by no other methods, no loss-pair measurement in actual networks has ever been reported. We first characterize the residual packet's delay by including other important factors (such as the impact of the first packet in the pair) which were ignored before. As a consequence, we invalidate a previous claim that measurement based on the second packet gives the same result as that based on the first. Second, we employ HTTP/OneProbe to measure from a single endpoint all four possible loss pairs for a round-trip network path. We have conducted loss-pair measurement for 88 round-trip paths continuously for almost three weeks. Being the first set of loss-pair measurement in the Internet, we have obtained a number of original results, such as prevalence of loss pairs, distribution of different types of loss pairs, and effect of route change on the paths' congestion state.