This paper studies the capacity of the two-user intensity-modulation/direct-detection (IM/DD) interference channel (IC), which is relevant in the context of multi-user optical wireless communications. Despite some known single-letter capacity characterizations for general discrete-memoryless ICs, a computable capacity expression for the IM/DD IC is missing. In this paper, we provide tight and easily computable inner and outer bounds for a general two-user IM/DD IC under peak and average optical intensity constraints. The bounds enable characterizing the asymptotic sum-rate capacity in the strong and weak interference regimes, as well as the generalized degrees of freedom (GDoF) in the symmetric case. Using the obtained bounds, the GDoF of the IM/DD IC is shown to have a `W' shape similar to the Gaussian IC with power constraints. The obtained bounds are also evaluated numerically in different interference regimes to show their tightness, and used to study the performance of on-chip and indoor OWC systems.