We explore the evolution of solar activity for next several sunspot cycles beyond 2016 using data for the geomagnetic indices aa/Ap and the solar polar magnetic field intensity for shorter time intervals; the indices are related to the solar wind and do not depend on Earth's climate. We find that the baseline of the geomagnetic indices increases monotonically from 1900 to 1986 and declines afterwards. We speculate that a cycle with a period ∼86 × 2 = 172y may exist in aa/Ap. If one assumes that solar wind will exhibit the same periodicity for the rest of the twenty-first century, one should expect the next uptick of the aa/Ap timeline to occur in the seventies. In the mean time, the indices Ap/aa may continue to undergo three-cycle-quasi-periodicity (TCQP) to a value lower than in early 1900s, due to a steeper slope during the last few solar cycles compared to that of the period before 1900; it may reach the grand minimum level. Solar polar magnetic field intensity is decreasing systematically for the last three cycles (22–24) as are the sunspot numbers at the cycle peak. Livingston and Penn (2009) note a long term weakening of maximum sunspot magnetic field since 1992. North-South (N-S) asymmetry in the polar field strength is most pronounced for the decay phase of cycles 23, 24; it seems to change sign after cycle 21. These trends have great implications for solar physics and future space weather/climate. We are unable to anticipate the degree and future change of sign of the N-S asymmetry of the solar polar field at present time.