This paper studies airline customers' online search and purchase behaviors. Two fundamental aspects of online behavior are examined: (1) the link between search behavior and buying behavior and (2) the evolution of inter-temporal search and purchase decisions of strategic buyers. In the first study, we examine online customers' dynamic conversion behaviors using clickstream data. A new model based on Markov chains that incorporates discrete choices and decision-timing is proposed to capture key search effects on consumer decisions as well as dynamics of browsing behavior both within and across visits. Empirical results show that within-site search activities lead to strong consumer engagement and thus increase purchase and revisit propensities. Fit comparison between first and second order Markov chains allows us to conclude that consumer decisions are primarily influenced by the current search. Furthermore, we observe that consumers dynamically adjust their browsing behavior both within and across visits. The second study investigates the evolution of inter-temporal search and purchase decisions of strategic buyers. Risk neutral buyers follow simple behavioral rules based on future and current prices and options available. We show that the trade-off between waiting and purchasing will become less and less favorable to waiting. Price elasticity should therefore drop as departure date approaches. With stationary price distributions, search and purchase efforts increase with proximity to the deadline. We extend the base model to allow for price evolution and demand uncertainty. We find that increases in mean price and price dispersion may attenuate increasing propensities for search and purchase. We demonstrate our models through a logit estimation on a unique data set from a major online travel agency.