In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.