The interplanetary magnetic field (IMF) has its origin in open magnetic regions of the Sun (coronal holes). The location of these regions and their total open flux &PHgr;open can be inferred from current-free extrapolations of the observed photospheric field. We derive the long-term variation of &PHgr;open during 1971--1998 and discuss its causes. Near sunspot minimum, the open flux originates mainly from the large polar coronal holes, whereas at sunspot maximum it is rooted in small, lower-latitude holes characterized by very high field strengths; the total amount of open flux thus remains roughly constant between sunspot minimum and maximum. Through most of the cycle, the variation of &PHgr;open closely follows that of the Sun's total dipole strength, showing much less dependence on the total photospheric flux or the sunspot number. However, episodic increases in large-scale sunspot activity lead to strengthenings of the equatorial dipole component, and hence to enhancements in &PHgr;open and the IMF strength lasting typically ~1 yr. ¿ 2000 American Geophysical Union