Research on open innovation suggests that companies benefit differentially from adopting open innovation strategies; however, it is unclear why this is so. One possible explanation is that companies' business models are not attuned to open strategies. Accordingly, we propose a contingency model of open business models by systematically linking open innovation strategies to core business model dimensions, notably the content, structure, governance of transactions. We further illustrate a continuum of open innovativeness, differentiating between four types of open business models. We contribute to the open innovation literature by specifying the conditions under which business models are conducive to the success of open innovation strategies.