INTRODUCTION The birth of Space Physics occurred explosively in October 1957 with the launch of Sputnik 1 into low Earth orbit. Since then, in-situ observations and measurements of the matter outside Earth became possible by instrumentation on board a fleet of artificial spacecraft following Sputnik 1 in quick succession. Half a century later we are now in possession of a pretty complete overall knowledge of the state of matter in interplanetary space. A multitude of spacecraft monitored the space far out, most recently up to the bounds of the heliosphere accumulating a huge amount of data and discovering a large number of effects which are completely alien to the laboratory. The era of discoveries and their theoretical interpretation is ongoing; it has even accelerated, being supported by the modern means of massive data acquisition and analysis, computing, numerical methods and numerical simulation techniques. Nevertheless, though we witnessed an enormous progress in our knowledge and understanding of the phenomena occurring space, quite a number of the originally raised fundamental questions remain only partially answered or even unanswered altogether. They have become much more detailed than before as our knowledge and understanding has penetrated deep into the microscopic state of the phenomena, but the phenomena themselves have just been monitored without bringing them to their ultimate solution. In the following we list a few of the questions that still await their final answer and thus challenge the future of space physics. Our list will necessarily remain incomplete and be biased by our own preferences, though. ORIGIN OF THE SOLAR WIND Parker (1958) developed a stationary fluid theory of supersonic outflow from the solar corona, being accelerated and passing through a critical point to supersonic velocities. The mechanism of acceleration was hypothetical and remains unknown until today. Any material to leave the Sun must be accelerated to speeds large enough for overcoming the gravitational attraction at the solar surface, i.e., >620 km/s. Thermal models won’t do, as has been understood early. In fact, the average radial solar wind speed at a distance of 1 AU is 400 km/s, occasionally reaching 1000 km/s and more. Various kinds of plasma waves, plasma turbulence including residual collisions have been invoked for the ultimate acceleration mechanism (for a review see Burgess et al., 2013); however, none of the proposals comes up for the quasi-steadiness, persistence and comparatively large number of particles accelerated from the solar corona into the solar wind. Other ideas called for microflares (Gold, 1964) or even nanoflares (Parker, 1972) in the lower corona or upper chromosphere, i.e., small reconnection events that occur almost continuously and contribute a continuous upward flow of matter. However, the evidence for such models is sparse and, in addition, the ultimate flare mechanism remains as well unknown, which implies that the problem is only shifted to another unexplained phenomenon. In this respect the observations of the Ulysses mission have become important, which surrounded the Sun on a unique orbit almost perpendicular to the ecliptic plane. Ulysses confirmed that the solar wind is a two-state phenomenon (McComas et al., 1998) finding that the fast solar wind originates in coronal holes at polar latitudes (Balogh and Smith, 2001), where it is accelerated in the lower corona to high speeds, large momentum and energy content on open magnetic field lines. Conversely, the slow solar wind originates from regions where the coronal magnetic field appears closed, as revealed by composition studies (von Steiger et al., 2000). Its much higher variability in all parameters points to an altogether different origin than the fast wind, possibly by quasi-stationary reconnection of open magnetic field lines migrating along the coronal streamer belt (Fisk et al., 1998a). Coronal mass ejections (CMEs), cases of sometimes extreme solar outbursts with large amounts of matter ejected into space, preferentially also occur from these regions. The reason for such enormous mass ejections is not fully known (for reviews see Kunow et al., 2007). It may be related to the action of reconnection in the deeper layers of the coronal magnetic field, which destabilizes large coronal loops. Reconnection is assumed to be the dominant energy release mechanism of flares, as it already was in the micro-flare model. Possibly reconnection, maybe in combination with other phenomena like plasma heating to high temperatures etc., is indeed the primary driver of the solar wind. However, the origin of the solar wind remains one of the great mysteries of space physics and poses a challenge for this century. Possibly all three phenomena, CMEs, flares, and the acceleration of the solar wind are just different facets of the same problem.