TLS and the applications it secures (eg, email, online banking, social media) rely on the web PKI to provide authentication. Without strong authentication guarantees, a capable attacker can impersonate trusted network entities and undermine both data integrity and confidentiality. At its core, the web PKI succeeds as a global authentication system because of the scalability afforded by trust. Instead of requiring every network entity to directly authenticate every other network entity, network entities trust certification authorities (CAs) to perform authentication on their behalf. Prior work has extensively studied the TLS protocol and CA authentication of network entities (ie, certificate issuance), but few have examined even the most foundational aspect of trust management and understood which CAs are trusted by which TLS user agents, and why. One major reason for this disparity is the opacity of trust management in two regards: difficult data access and poor specifications. It is relatively easy to acquire and test popular TLS client/server software and issued certificates. On the other hand, tracking trust policies/deployments and evaluating CA operations is less straightforward, but just as important for securing the web PKI. This dissertation is one of the first attempts to overcome trust management opacity. By observing new measurement perspectives and developing novel fingerprinting techniques, we discover the CAs that operate trust anchors, the default trust anchors that popular TLS user agents rely on, and a general class of injected trust anchors: TLS interceptors. This research not only facilitates new ecosystem visibility, it also provides an empirical grounding for trust management specification and evaluation. Furthermore, our findings point to many instances of questionable, and sometimes broken, security practices such as improperly identified CAs, inadvertent and overly permissive trust, and trivially exploitable injected trust. We argue that most of these issues stem from inadequate transparency, and that explicit mechanisms for linking trust anchors and root stores to their origins would help remedy these problems.