Throughout months of extremely low solar activity during the recent extended solar-cycle minimum, structural evolution continued to be observed from the Sun through the solar wind and to the Earth. In 2008, the presence of long-lived and large low-latitude coronal holes meant that geospace was periodically impacted by high-speed streams, even though solar irradiance, activity, and interplanetary magnetic fields had reached levels as low as, or lower than, observed in past minima. This time period, which includes the first Whole Heliosphere Interval (WHI 1: Carrington Rotation (CR) 2068), illustrates the effects of fast solar-wind streams on the Earth in an otherwise quiet heliosphere. By the end of 2008, sunspots and solar irradiance had reached their lowest levels for this minimum (e.g., WHI 2: CR 2078), and continued solar magnetic-flux evolution had led to a flattening of the heliospheric current sheet and the decay of the low-latitude coronal holes and associated Earth-intersecting high-speed solar-wind streams. As the new solar cycle slowly began, solar-wind and geospace observables stayed low or continued to decline, reaching very low levels by June -aEuro parts per thousand July 2009. At this point (e.g., WHI 3: CR 2085) the Sun-Earth system, taken as a whole, was at its quietest. In this article we present an overview of observations that span the period 2008 -aEuro parts per thousand 2009, with highlighted discussion of CRs 2068, 2078, and 2085. We show side-by-side observables from the Sun's interior through its surface and atmosphere, through the solar wind and heliosphere and to the Earth's space environment and upper atmosphere, and reference detailed studies of these various regimes within this topical issue and elsewhere.