We develop a theoretical analysis of an entrepreneur's choice between venture capital (VC) and angel financing at various stages in a private firm's life, and characterize the dynamic evolution of the firm's contract with its financier (VC or angel). In our model, an entrepreneur has information superior to a potential financier about his own firm; however, this information advantage diminishes as the financier interacts with the firm over time. Venture capitalists and angels differ in two ways. First, venture capitalists can add value to the firm by exerting effort, which, together with the entrepreneur's effort, increases the chance of project success; the angel is unable to add significant value. Second, venture capital financing is scarce relative to angel financing. The equilibrium VC contract maximizes value-addition by ensuring that both the entrepreneur and the VC exert optimal effort. We develop the following results in the above setting. First, we characterize the optimal financing path of the firm: depending on firm characteristics, a firm may use angel financing in its early stages and switch to VC financing in later stages, or vice versa. Second, VC financing contracts resemble convertible debt, while angel financing contracts may resemble a variety of financial securities, including equity. Third, for firms which use venture financing in earlier as well as later rounds, earlier round financing contracts will have more of a fixed income component and less of a warrant (upside) component compared to later round financing contracts. Fourth, later round financing contracts between an entrepreneur and a VC who financed it in an earlier round will have a greater warrant component compared to such a contract between a VC and a previously angel-financed firm. Fifth, we characterize how the structure of VC financing contracts relate to: (i) the experience and productivity of the VC; (ii) the nature of the firm's industry; and (iii) the scarcity of VC financing. Finally, we develop predictions for the relationship between the financing path of a firm and the probability of its having a successful exit (IPO or acquisition), and for differences in the compositions of VCs' and angels' investment portfolios.