The model of a Local Hot Bubble has been widely accepted as providing a framework that can explain the ubiquitous presence of the soft X-ray background diffuse emission. We summarize the current knowledge on this local interstellar region, paying particular reference to observations that sample emission from the presumed local million degree K hot plasma. However, we have listed numerous observations that are seemingly in conflict with the concept of a hot Local Bubble. In particular, the discovery of solar wind charge exchange that can generate an appreciable soft X-ray background signal within the heliosphere, has led to a reassessment of the generally accepted model that requires a hot local plasma.In order to explain the majority of observations of the local plasma, we forward two new speculative models that describe the physical state of the local interstellar gas. One possible scenario is similar to the present widely accepted model of the Local Hot Bubble, except that it accounts for only 50% of the soft X-ray emission currently detected in the galactic plane, has a lower thermal pressure than previously thought, and its hot plasma is not as hot as previously believed. Although such a model can solve several difficulties with the traditional hot Local Bubble model, a heating mechanism for the dimmer and cooler gas remains to be found. The second possible explanation is that of the 'Hot Top' model, in which the Local Cavity is an old su-B.Y. Welsh ( ) Space Sciences Laboratory, University of California, 7 Gauss Way, Berkeley, CA 94720, USA e-mail: bwelsh@ssl.berkeley.edu R.L. Shelton Department of Physics and Astronomy, University of Georgia, Athens, GA 30602, USA pernova remnant in which no (or very little) million degree local plasma is presently required. Instead, the cavity is now thought to be filled with partially ionized cloudlets of temperature ∼ 7000 K that are surrounded by lower density envelopes of photo-ionized gas of temperature ∼ 20,000 K. Although this new scenario provides a natural explanation for many of the observations that were in conflict with the Local Hot Bubble model, we cannot (as yet) provide a satisfactory explanation or the emission levels observed in the B and Be ultra-soft X-ray bands.