This dissertation consists of two essays. The first, titled “Sweep Order and the Cost of Market Fragmentation” takes a “revealed-preference” approach towards gauging the effects of market fragmentation by documenting the implicit costs borne by traders looking to avoid executing in a fragmented environment. I show that traders use Intermarket Sweep Orders (ISO) to trade “as-if” markets were single-venued and pay a premium to do so. Using a sample of over 2,600 securities over the period January 2019 to April 2021, this premium amounts to 1.3 bps on average (or 40%of the effective spread), amounting to a total of $3 billion over the sample period. I find a positive, robust, and significant relationship between the premium and different measures of market fragmentation, further supporting the interpretation of the premium as a cost of market fragmentation. The second essay, titled “The Profitability of Liquidity Provision” investigates the relationship between the profits realized from providing liquidity and the amount of time it takes liquidity providers to reverse their positions. By tracking the cumulative inventory position of all passive liquidity providers in the US equity market and matching each aggregate position with its offsetting trade, I construct a measure of profits to liquidity provision (realized profitability) and assess how profitability varies with the average time to offset. Using a sample of all common stocks from 2017 to 2020, I show that there is substantial variation in the horizon at which trades are turned around even for the same stock. As a mark-to-market profit, the conventional realized spread—measured with a prespecified horizon—can deviate significantly from the realized profits to liquidity provision both in the cross-section and in the time-series. I further show that, consistent with the risk-return tradeoff faced by liquidity providers as a whole, realized profitability is low for trades that are quickly turned around and high for trades that take longer to reverse.