The Sun is an active and variable star. Instabilities and non-stationary processes connected to the solar magnetic field and its evolutionary mechanisms modify its radiative and particle output on different time scales, from seconds to the evolutionary scale of the star. The Sun's activity affects interplanetary space and planetary environments, through space weather due to short-term activity and space climate on longer timescales. Space weather processes and forecasts are therefore important for both Earth and space within the heliosphere. The multi-disciplinary IAU Symposium 335 on 'Space Weather of the Heliosphere: Processes and Forecasts' gave a balanced overview of the general advances in space weather. It linked various aspects of research in solar, heliospheric and planetary physics, emphasizing cross-disciplinary developments. These companion proceedings, covering interdisciplinary topics and attracting a wide variety of contributors, serves as a timely reference to the international space weather community.