It's a slightly tough question that can't be answered with a simple "they share X characteristic in common". It's more that some of them share a characteristic, and some of those share a characteristic with another load of species within the same sub-clade, and some of the characteristics they have are shared with some more... etc.
The American Journal of Botany puts it:
(Synapomorphy: a shared trait believed to have been present in a common ancestor.)
Currently, no unambiguous morphological synapomorphies have been confidently identified as defining the Eucalypteae in comparison to other
Myrtaceae (however, see Wilson et al., 2001 , for some possibilities).
Within the Eucalypteae, however, subclades are defined by
synapomorphies. For instance, Angophora Cav., Corymbia , and
Eucalyptus share several possible synapomorphies, such as presence of
oil glands that protrude above the surface of the epidermis (“emergent
oil glands” of Ladiges, 1984 ).
These are modified into distinctive
bristle glands in Angophora and Corymbia ( Johnson, 1972 ; Ladiges,
1984 ), which are a unique synapomorphy for the Angophora - Corymbia
clade ( Ladiges et al., 1995 ; Wilson et al., 2001 ). Angophora ,
Corymbia , and Eucalyptus are also characterized by having compound
petals and, in Eucalyptus, a portion of the compound petal is usually
modified into a staminophore, or stamen-bearing tissue ( Drinnan and
Ladiges, 1988 , 1989a , b , 1991a ).
Other characters are apomorphic
but are likely homoplasious, having arisen more than once within
Eucalypteae. For example, some Corymbia and Eucalyptus species are
characterized by the presence of calycine and/or corolline opercula,
or cap-like perianth whorls that are deciduous from the flower at or
prior to anthesis (e.g., Johnson, 1972 ; Hill and Johnson, 1995 ;
Boland et al., 2006 ). Opercula likely have separate origins in these
genera ( Ladiges et al., 1995 ; Parra-O. et al., 2009 ). A caducous
calyx that usually leaves a scar on the flower bud (see Johnson, 1972
; Boland et al., 2006 ) is also an apomorphic but homoplastic
character within Eucalypteae, being a synapomorphy for a clade within
Corymbia ( Ladiges et al., 1995 ; Parra-O. et al., 2009 ) and having
arisen at least once on the stem of Eucalyptus subgenus Symphyomyrtus
( Fig. 1B ).