This paper has four chapters. The first chapter serves as an introduction. The second chapter studies the transaction fees in the bitcoin system. The transaction fees and transaction volume in the bitcoin system increase whenever the network is congested and results from a simple VAR show that it is indeed the case. To account for the empirical findings, we build a model where users and miners together determine the transaction fee and transaction volume endogenously. Even though the fluctuating transaction fee mechanism in bitcoin introduces the extra cost of uncertainty to users, a back-of-envelope calculation shows that the cost of using the bitcoin network for transactions is still smaller than the cost of using the current conventional payment system with a fix transaction fee rate. The second chapter studies the time-varying price dispersion among different bitcoin exchanges. We identify the sources of price dispersion using a standard time-varying vector autoregression model with stochastic volatility. The results show that shocks to transaction fees and bitcoin price growth explain on average 20%, and sometimes more than 60%, of the variation of price dispersion. The third chapter studies the relationship between connections and returns in the bitcoin investor network. Using transaction data from the bitcoin blockchain, we reach three conclusions. First, on average, the annualized returns of connected addresses in the network are 20.75% above those of their unconnected peers. Second, returns also differ among those connected addresses. By dividing the connected ad- dresses into ten deciles based on their centrality, we find that addresses in the two most-connected deciles earn higher returns than the other connected addresses. Third, eigenvector centrality is more related than degree centrality to higher returns, implying that quality of connections matters.