In this dissertation, I investigate various aspects of auction design problems. In Chapter 1, I study secret reserve prices in auctions that are partially binding in the sense that the sellers can accept bids below them. Such a reserve price has a bite only when the winning bid exceeds it, in which case the winning bid is accepted without seller's action. This work investigates the motivation for this puzzling practice that many real-world auctions take, such as wholesale used-car auctions. I estimate a structural model of ascending auctions using the auction data in the wholesale used-car market. To microfound seller's decision of the secret reserve price, I posit that the seller has uncertainty as to the value of the item when she sets the reserve price and that this uncertainty is resolved after she observes the auction price. I compare the status quo with two counterfactual auction formats: (i) no reserve prices and the seller gets to accept or reject every winning bid, and (ii) the seller commits to the secret reserve price. I observe very little difference among them in terms of probability of trade, seller's payoff and revenue. I discuss how the current format may be rationalized as reducing transaction costs for asking sellers' confirmation of all winning bids and avoiding sellers' cognitive cost of committing to a reserve price. The work in Chapter 2 is a joint work with Gabriel Y. Weintraub, Ralph A. Mastromonaco, and Samuel S. Seljan. Weintraub and I formulated the research questions and laid out steps for the research project in close collaboration, and I performed all the data analysis with the advice from Weintraub. Mastromonaco and Seljan provided Weintraub and me with the dataset and the necessary domain knowledge. In this work, we study actual bidding behavior when a new auction format gets introduced into the marketplace. More specifically, we investigate this question using a novel dataset on internet display advertising auctions and exploiting a staggered adoption by different publishers (sellers) of first-price auctions (FPAs), instead of the traditional second-price auctions (SPAs). Event study regression estimates indicate that, immediately after the auction format change, the revenue per sold impression (price) jumped considerably for the treated publishers relative to the control publishers, ranging from 35% to 75% of the pre-treatment price level of the treatment group. Further, we observe that in later auction format changes the increase in the price levels under FPAs relative to price levels under SPAs dissipates over time, reminiscent of the celebrated revenue equivalence theorem. We take this as evidence of initially insufficient bid shading after the format change rather than an immediate shift to a new Bayesian Nash equilibrium. Prices then went down as bidders learned to shade their bids. We also show that bidders' sophistication impacted their response to the auction format change. Our work constitutes one of the first field studies on bidders' responses to auction format changes, providing an important complement to theoretical model predictions. As such, it provides valuable information to auction designers when considering the implementation of different formats. In Chapter 3, I study the efficient design of mortgage foreclosure auctions. Lenders with delinquent mortgages recover their lending by foreclosure, which is a legal process to sell the mortgage property via public auction. In the U.S., mortgage lenders are allowed to bid in such foreclosure auctions, and they win in such auctions very frequently. I study the question of why mortgage lenders win in most of those auctions. I develop a theoretical model of ascending auctions with private values. I find that the lender's optimal bidding strategy is the same as the optimal reserve price of an auction seller, if it is below the debt balance. In other words, the lender exercises monopoly power as would an auction seller, up to the remaining debt. This increases the probability that the lender wins the auction, as third-party bidders' optimal strategy is to drop out of the auction when the price reaches their respective valuations of the mortgage property. The monopoly power that the mortgage confers to the lender also implies that the resulting allocation of the mortgage property may be inefficient. To resolve such inefficiency, I derive a mechanism that achieves efficient allocation of the foreclosed property.