In the past decade, a consensus has emerged regarding the nature of classicalBe stars: They are very rapidly rotating main sequence B stars, which, througha still unknown, but increasingly constrained process, form an outwardlydiffusing gaseous, dust-free Keplerian disk. In this work, first the definitionof Be stars is contrasted to similar classes, and common observables obtainedfor Be stars are introduced and the respective formation mechanisms explained.We then review the current state of knowledge concerning the central stars asnon-radially pulsating objects and non-magnetic stars, as far as it concernslarge scale, i.e., mostly dipolar, global fields. Localized, weak magneticfields remain possible, but are as of yet unproven. The Be phenomenon, linkedwith one or more mass ejection processes, acts on top of a rotation rate ofabout 75% of critical or above. The properties of the process can be wellconstrained, leaving only few options, most importantly, but not exclusively,non-radial pulsation and small scale magnetic fields. Of these, it is wellpossible that all are realized: In different stars, different processes may beacting. Once the material has been lifted into Keplerian orbit, memory of thedetails of the ejection process is lost, and the material is governed byviscosity. The disks are fairly well understood in the theoretical framework ofthe viscous decretion disk model. This is not only true for the disk structure,but as well for its variability, both cyclic and secular. Be binaries arereviewed under the aspect of the various types of interactions a companion canhave with the circumstellar disk. Finally, extragalactic Be stars, at lowermetallicities, seem more common and more rapidly rotating.
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