The Sun and its solar wind are currently exhibiting extremely low densities and magnetic field strengths, representing states that have never been observed during the space age. The highly abnormal solar activity between cycles 23 and 24 has caused the longest solar minimum in over 80 years and continues into the unusually small solar maximum of cycle 24. As a result of the remarkably weak solar activity, we have also observed the highest fluxes of galactic cosmic rays in the space age and relatively small solar energetic particle events. We use observations from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) on the Lunar Reconnaissance Orbiter to examine the implications of these highly unusual solar conditions for human space exploration. We show that while these conditions are not a show stopper for long‐duration missions (e.g., to the Moon, an asteroid, or Mars), galactic cosmic ray radiation remains a significant and worsening factor that limits mission durations. While solar energetic particle events in cycle 24 present some hazard, the accumulated doses for astronauts behind 10 g/cm2 shielding are well below current dose limits. Galactic cosmic radiation presents a more significant challenge: the time to 3% risk of exposure‐induced death (REID) in interplanetary space was less than 400 days for a 30 year old male and less than 300 days for a 30 year old female in the last cycle 23–24 minimum. The time to 3% REID is estimated to be ∼20% lower in the coming cycle 24–25 minimum. If the heliospheric magnetic field continues to weaken over time, as is likely, then allowable mission durations will decrease correspondingly. Thus, we estimate exposures in extreme solar minimum conditions and the corresponding effects on allowable durations.