In many applications, decision makers must dynamically manage limited resource capacities to satisfy random requests arriving sequentially over time. Examples include routing e-commerce orders across fulfillment centers; dispatching drivers in shared mobility systems; and allocating fare classes across airline networks. The standard network revenue management abstraction used to model such problems is as follows. We have various products, each with a unique revenue, and a set of resources, each with limited capacity. Each product consumes a certain combination of resources. We have a selling horizon with multiple time periods during which requests for products arrive stochastically. The decision maker must decide, at each arrival of product request, whether to accept or reject the request. If the request is accepted, a revenue will be generated and capacities of the resources used by that product will be consumed. If the request is rejected, the customer will leave the system. The objective is to maximize total expected revenue from accepted requests over the horizon subject to the capacity constraints of the resources. Although we have decades of work on such standard revenue management problems, existing research faces two fundamental difficulties in practice. First, from a modeling perspective, traditional revenue management models assume that customer arrivals (demand) follow a discrete-time approximation to a Poisson process. Under such a demand model, the total number of arrivals is highly concentrated around its mean. This assumption is commonly violated in real-world data, where the total number of arrivals often exhibits high variability. Second, under Poisson demand models, arrivals in non-overlapping intervals of time are independent of each other. This too is often violated in practice, as demand frequently exhibits strong temporal correlations. On the other hand, from an algorithmic perspective, incorporating such general demand structures can be highly challenging. Under traditional demand models with Poisson arrivals, dynamic programming formulations of the revenue management problem are intractable due to the curse of dimensionality; thus, the existing work establishes performance guarantees for approximate policies driven by fluid approximations. However, it is conceivable that these performance guarantees are only achievable because Poisson arrivals imply that the demand variability is relatively small when the demand volume is large. Under non-Poisson arrivals with high variance and correlation between the number of arrivals over different time intervals, it is not clear whether we can design fluid approximations that yield policies with performance guarantees. This work fills these important gaps in both modeling and algorithmic perspectives. In this dissertation, we first consider a calendar-aware demand model that addresses the limitations of the traditional Poisson demand model mentioned above and allows high variance and temporal correlation in demand. Reflecting the structure of practical forecasting systems, our calendar-aware model partitions the selling horizon into several stages, each representing a standard time interval such as a week. We use a general random variable to capture the number of customer arrivals in each stage. This random variable can have arbitrary distribution capturing non-Poisson arrivals and high variability in the number of arrivals. Moreover, we allow the random number of customer arrivals in different stages to be temporally correlated by letting the total number of arrivals in each stage follow a Markov process. We refer to this model as calendar-aware demand model because it explicitly incorporates the temporal dependence of the demand. We give a theoretically sound fluid approximation of the revenue management problem under the calendar-aware demand model in the sense that it yields asymptotically optimal policies. The form of our fluid approximation is surprising as its constraints use expected capacity consumption of a resource up to a certain time period, conditional on the demand in the stage just before the time period in question. We use the fluid approximation to give a policy such that as the resource capacities and number of stages in the problem increase with the same rate, the performance guarantee of the approximate policy converges to one. To our knowledge, this result gives the first asymptotically optimal policy under dependent demands with arbitrary distributions. Our computational experiments indicate that using the correct fluid approximation can make a dramatic impact in practice. Second, we study a Markov-modulated demand model that captures temporal correlations through an exogenous Markov chain. This Markov chain serves to model underlying factors that influence product demand, such as social media trends, weather conditions, and the economic environment. Our main contribution in this work is to develop a family of history-dependent fluid approximations, in which the probability of accepting a product request depends on the history of the Markov chain over the past $\theta$ periods. Our fluid approximations yield upper bounds on the optimal total expected revenue, and these upper bounds become tighter as we incorporate longer histories. Moreover, the approximate policies we construct from these fluid approximations also have better performance guarantees when we use longer histories in the fluid approximations. Lastly, we incorporate intertemporal constraints into our fluid approximations. In particular, we focus on monotone pricing constraints as a canonical and practically relevant form of intertemporal operational constraints. A monotone pricing constraint requires the price of each product to be either non-increasing or non-decreasing over time. Such constraints are well motivated by real-world applications. For example, such constraints occur when selling fashion or perishable items and the price for a product has to be decreasing over time, so that early purchasers pay premium. Whereas, airlines sometimes impose the opposite rule, offering only monotonically increasing prices to encourage advance bookings. Fluid-based pricing policies struggle to enforce such rules because they typically randomize their decisions independently across time periods. We address the monotone pricing constraints by introducing a novel fluid approximation. Our fluid approximation ensures that the probability distributions of the prices charged for a product at a given time period stochastically dominate those at earlier time periods. This dominance condition serves as a proxy for the requirement that the prices charged for each product must be monotonically increasing over time. Although our fluid approximation only enforces a stochastic dominance relationship between the distributions of prices across time, we can extract a pricing path that is monotonically increasing over the horizon. In particular, we recover such pricing paths from the LP solution using an inverse cumulative mass function construction. More interestingly, we show that this sampling procedure generates at most two monotonically increasing price paths for each product. The resulting policy achieves both a constant-factor performance guarantee and an asymptotic guarantee, where the asymptotic regime is defined by the capacity of the system scaling to infinity. The performance bound includes an additional term that quantifies the discrepancy in expected demand between the two candidate price paths. When this term is bounded, the policy approaches optimality as the minimum resource capacity grows.