Increasingly, temporally-detailed graphs are of a size, variety, and update rate that exceed the capability of current computing technologies. Such datasets can be called Big Temporally-Detailed Graph (Big-TDG) Data. Examples include temporally-detailed (TD) roadmaps which provide typical travel speeds experienced on every road segment for thousands of departure-times in a typical week. Likewise, we have temporally-detailed (TD) social networks which contain a temporal trace of social interactions among the individuals in the network over a time window. Big-TDG data has transformative potential. For instance, a 2011 McKinsey Global Institute report estimates that location-aware data could save consumers hundreds of billions of dollars annually by 2020 by helping vehicles avoid traffic congestion via next-generation routing services such as eco-routing. However, Big-TDG data presents big challenges for the current computer science state of the art. First, Big-TDG data violates the cost function decomposability assumption of current conceptual models for representing and querying temporally-detailed graphs. Second, the voluminous nature of Big-TDG data can violate the stationary ranking-of-candidate-solutions assumption of dynamic programming based techniques such Dijsktra's shortest path algorithm. This thesis proposes novel approaches to address these challenges. To address the first challenge, this thesis proposes a novel conceptual model called, "Lagrangian Xgraphs," which models non-decomposability through a series of overlapping (in space and time) relations, each representing a single atomic unit which retains the required semantics. An initial study shows that Lagrangian Xgraphs are more convenient for representing diverse temporally-detailed graph datasets and comparing candidate travel itineraries. For the second challenge, this thesis proposes a novel divide-and-conquer technique called "critical-time-point (CTP) based approach," which efficiently divides the given time-interval (over which over non-stationary ranking is observed) into disjoint sub-intervals over which dynamic programming based techniques can be applied. Theoretical and experimental analysis show that CTP based approaches outperform the current state of the art.