Inconsistency
<button md-icon-button>
  <md-icon>some_ligature</md-icon>
</button>
background should be transparent
<button md-icon-button>
  <md-icon>some_ligature</md-icon>
</button>
is not transparent
but
<a md-icon-button>
  <md-icon>some_ligature</md-icon>
</a>
is transparent
Inconsistency with the documentation and the behavior of  a & button
https://github.com/angular/material2/blob/master/src/lib/button/README.md
Alpha9-3
Both button and a have transparent background in current master. 
This appears to longer be true.  <button mat-icon-button> is not transparent to me.  I have @angular/material-5.2.3 installed.
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Most helpful comment
This appears to longer be true.
<button mat-icon-button>is not transparent to me. I have @angular/material-5.2.3 installed.