The recent advent of distribution-level phasor measurement units (D-PMUs), a.k.a.,micro-PMUs, has introduced a wide range of new applications to achieve situational awareness in power distribution systems. In this thesis, we seek to develop an effective optimization based and physics-conditioned data-driven techniques to enhance and protect these types of applications in power distribution systems against cyber-attacks, making them more robust and reliable. Three main topics are addressed with respect to the analysis of D-PMU measurements. In the first topic, we focus on an emerging sub-class of these applications that are called event-based situational awareness methods. We explore a scenario, where a cyberattack compromises the micro-PMU measurements during an event. We introduce a novel optimization-based method to detect the presence of the attack and then identify which micro-PMUs are compromised so as to discard the compromised measurements as a defense mechanism. In the second topic, we explore a new cyber-threat against data-driven event classification in micro-PMU measurements. In particular, we model and analyze the poisoning attack against the use of support vector machines (SVM) as the method of event classification; which has been used in practice to study distribution synchrophasors. We also propose an effective poisoning attack detection method in the available measurements. Finally, in the third topic, we propose a novel method to address the issue of low-observability in Distribution System State Estimation (DSSE). In this approach, we integrate the trained Generative Adversarial Network (GAN) models at the unobservable locations, together with the direct synchronized measurements at the observable locations, into the formulation of the DSSE problem. In this regard, we simultaneously take advantage of the forecasting capabilities of the GAN models, the available real-time synchronized measurements, and the DSSE formulations based on physical laws in the power system. Together, the above three methods contribute to achieving an efficient and secure monitoring system for power distribution networks, taking advantage of the synchronized measurements from micro-PMUs.