During the past decade, observational and theoretical studies have increasingly indicated that the extended circumgalactic medium (CGM), i.e., the gaseous halos extending several hundred kpc out from regions where stars are found, is an important component of galaxies that regulates their evolution. The CGM is likely the dominant reservoir of ordinary matter in galaxies at all epochs, and gas flows to and from the CGM surely have profound effects on the tip-of-the-iceberg stellar regions that most people think of as a “galaxy”. The light emitted by the CGM is extremely faint, so the most practical technique for exploring these dark backwaters is to study the absorption lines that they imprint on the spectra of background continuum sources. This talk will review several recent absorption-line studies of the CGM, which turns out to harbor some strange and difficult-to-explain entities. For example, while the CGM plasma is detected in species such as O VI and Ne VIII and is typically highly ionized, it is also profoundly cold – very high-resolution data show that upper limits on the gas temperature are a factor of 10-20 below the temperature where O VI is expected to exist. Moreover, disparate ions ranging from Mg I (ionization potential = 7.6 eV) up to Ne VIII (IP = 239.1 eV) are kinematically very well aligned and clearly have a strong physical relationship. Standard collisional or photoionization models are hard-pressed to explain these data, and more complex physics will probably need to be considered. This talk will also (briefly) present data that suggest some tantalizing connections between CGM and the star-formation properties of galaxies, and some remarks will be made on the type of instruments that will be needed in the future to obtain a more complete understanding of galaxies including the difficult-to-observe components.