For the last two decades, most financial markets have undergone an evolution toward elec- tronification. The market for corporate bonds is one of the last major financial markets to follow this unavoidable path. Traditionally quote-driven (that is, dealer-driven) rather than order-driven, the market for corporate bonds is still mainly dominated by voice trading, but a lot of electronic platforms have emerged that make it possible for buy-side agents to simul- taneously request several dealers for quotes, or even directly trade with other buy-siders. The research presented in this article is based on a large proprietary database of requests for quotes (RFQ) sent, through the multi-dealer-to-client (MD2C) platforms operated by Bloomberg Fixed Income Trading and Tradeweb, to one of the major liquidity providers in European corporate bonds. Our goal is (i) to model the RFQ process on these platforms and the resulting competition between dealers, (ii) to use the RFQ database in order to implicit from our model the behavior of both dealers and clients on MD2C platforms, and (iii) to study the influence of several bond characteristics on the behavior of market participants.