In this thesis, I study the two-sided marketplaces with intermediaries that can facilitate matching, search and trades. The first chapter considers the welfare and distributional consequences of introducing the student-proposing deferred acceptance mechanism in a model where schools have exogenous qualities and the benefit from attending a school is supermodular in school quality and student type. Unlike neighborhood assignment, deferred acceptance induces non-positive assortative matching where higher-type students do not necessarily choose neighborhoods with better schools. Student types are more heterogeneous within neighborhoods under deferred acceptance. Assuming an elastic housing supply, deferred acceptance benefits residents in lower-quality neighborhoods with more access to higher quality schools. Moreover, more parents will `vote with their feet' for deferred acceptance, other things equal, than for neighborhood assignment. The second chapter studies a search platform in a setting where buyers search for sellers directly or through a platform with lower search costs, and the platform charges both sides for the transactions it facilitates. While many intermediaries attract as many users as possible by lowering search cost, potential buyers also care about how attractive the sellers available via the intermediary are, not just the number. A search platform's strategy is determined by the coexisting positive and negative cross-group externalities: (i) while buyers appreciate more choices of sellers available on the platform, (ii) increasing the number of available sellers makes the search for low-priced and high-value sellers harder due to an unfavorable price dispersion. A platform optimally adopts a threshold strategy of targeting sellers with lower costs to balance the competing externalities. The third chapter studies intermediation in a buyer-seller network with sequential bargaining. An intermediary matches traders connected in a network to bargain over the price of heterogeneous goods and has the freedom to charge each side commission. A profit-maximizing middleman can help eliminate trading delays but limits trade executed that are not surplus maximizing. When the middleman competes with the buyers and sellers being matched through an exogenous search process, she matches buyer and seller pairs that are selected less often by the exogenous search process.