This dissertation consists of three essays studying on over-the-counter trading (OTC henceforth). In Chapter 1, I model the formation of the inter-dealer network in an OTC market, and study how the network affects prices and volumes in the market. The model explains the empirically observed core-periphery network with dealers' capacity of providing liquidity. Specifically, dealers with large capacity comprise the core of the network, connecting them to all other dealers, while dealers who have small capacity operate at the periphery. In addition, my model matches the empirical finding on the negative relation between markups and order sizes. Furthermore, I show that there may be structural breaks in this negative relationship as variations in order sizes may alter the inter-dealer network. These results suggest that empirical studies on OTC markets should control for the stability of an inter-dealer network to avoid model misspecification. Chapter 2 evaluates how a centralized market could provide an incentive for OTC dealers to reduce opacity in trading. In this chapter, opacity is modeled as Knightian uncertainty faced by investors. I find that while a competitive centralized market provides an incentive for dealers to reduce opacity in an OTC market, a noncompetitive centralized market does the opposite. Competition between the competitive centralized market and the OTC market forces dealers in the latter to reduce opacity. With the noncompetitive centralized market, opportunities for collusion provide an incentive for dealers to increase opacity. Dealers do not have the incentive to reduce opacity in this case. In Chapter 3, we test the model implications in Chapter 2 with an empirical study on the corporate bond markets, and find consistent results. We find that transaction costs of bonds traded only in OTC markets are significantly different from (10 basis points larger than) bonds traded both in OTC markets and the NYSE market. Since the latter contains pre-trade information from the NYSE market, this finding suggests that pre-trade transparency reduces bonds' trading costs. This result implies that pre-trade transparency benefits investors but hurts dealers, as the major part of dealers' profits comes from investors' trading costs. We also find that pre-trade transparency increases bonds' values. Bonds with the NYSE pre-trade transparency have significantly lower bond yields than bonds without the pre-trade transparency. Our findings are robust to endogeneity of firms' bond listing decisions on the NYSE.