A model of the Oort cloud has been developed by accounting for planetary, stellar and Galactic perturbations using numerical symplectic integrations covering 4.5 Gyr. The model is consistent with the broad dynamical characteristics of the observed cometary populations injected from the Oort cloud into different regions of the Solar system. We show that the majority of observed high‐eccentricity trans‐Neptunian objects, Centaurs and short‐period comets have visited the Oort cloud (a > 1000 au) during their dynamical history. Assuming from observations that the near‐parabolic flux from the Oort cloud with absolute magnitudes H₁₀ < 7, perihelion distances q < 5 au and a > 10⁴ au is approximately 1 comet per year, our calculations imply a present Oort cloud population of ∼5 × 10¹¹ comets with H₁₀ < 10.9. Roughly half this number have a > 10⁴ au. The number of comets reaching the planetary region from the Oort cloud (a > 1000 au) is more than an order of magnitude higher per unit perihelion distance immediately beyond Neptune than in the observable zone q < 5 au. Similarly, the new‐comet flux from the Oort cloud per unit perihelion distance is a few tens of times higher in the near‐Neptune region than in the observable zone. The present number of high‐eccentricity trans‐Neptunian objects (q > 30 au and 60 < a < 1000 au) originating from the Oort cloud is in the approximate range 1–3 × 10¹⁰, depending on details of the initial model. A substantial fraction of these have a > 200 au and/or q > 40 au, and they are found mostly to originate from initial orbits with 25 < q < 36 au. Similarly, the number of Centaurs produced from the Oort cloud, where we define Centaurs to have 5 < q < 28 au and a < 1000 au, is smaller by a factor of 20–30. About 90 per cent of these Centaurs have a > 60 au. Objects that have visited the Oort cloud represent a substantial fraction of the Jupiter‐family comet population, achieving short‐period orbits by a process of gradual dynamical transfer, including a Centaur stage, from the outer Solar system to near‐Earth space. A similar mechanism produces Halley‐type comets, in addition to the well‐known diffusion process operating at small perihelion distances.