Context. Interstellar dust (ISD) is a major component in the formation and evolution of stars, stellar systems, and planets. Astronomical observations of interstellar extinction and polarization, and of the infrared emission of the dust, are the most commonly used technique for characterizing interstellar dust. Besides this, the interstellar dust from the local interstellar cloud enters the solar system owing to the relative motion of the Sun with respect to this cloud. Once in the solar system, in-situ observations can be made by spacecraft using impact ionization detectors and time-of-flight spectrometers like the ones flown on the Cassini, Ulysses, and Galileo, spacecrafts. Also a sample return can be done, as in the Stardust mission. Once in the solar system, the trajectories of these dust grains are shaped by gravitational, solar radiation pressure, and Lorentz forces. The Lorentz forces result from the interaction of the charged dust particles with the interplanetary magnetic field. The ISD densities in the solar system thus depend both on the location in the solar system and on time, correlated to the solar cycle. Aims. This paper aims at giving the reader insight into the flow patterns of ISD when it moves through the solar system. This is useful for designing future in-situ or sample return missions or for knowing whether for specific missions, simplified assumptions can be used for the dust flux and direction, or whether full simulations are needed. Methods. We characterize the flow of ISD through the solar system using simulations of the dust trajectories. We start from the simple case without Lorentz forces and expand to the full simulation. We pay attention to the different ways of modeling the interplanetary magnetic field and discuss the influence of the dust parameters on the resulting flow patterns. Dust densities, fluxes, and directionalities are derived from the trajectory simulations. Different graphics representations are used to gain insight into the flow patterns. As an illustration of how the model can be used, we predict the fluxes and directionalities of the ISD for the Cassini mission. Results. The characteristics of the flow of ISD through the solar system have been investigated to gain insight in the patterns of the flow. The modeling can also be used for predicting dust fluxes for different space missions or planets, and for understanding spacecraft measurements, such as those from Ulysses, Cassini, and Stardust.