Clearfix Show archive.org snapshot is a hack to clear floating elements without additional HTML markup.
If you only need to support IE8 and above, a great clearfix with few side effects is:
=clearfix
  &:after
    content: ""
    display: block
    clear: both
This is a Sass mixin.
Issues clearing with display: table
You will find many clearfix solutions that clear with display: table instead:
=clearfix
  &:after
    content: ""
    display: table
    clear: both
The problem with this solution is that they prevent collapsing margins from non-floating children of the cleared container.
See 
  this Codepen
  
    Show archive.org snapshot
  
 for a visualization of the differences between display: block and display: table.
See this article Show archive.org snapshot for more discussion.
Issues with Compass-provided clearfix
Compass also gives you a mixin from compass/utilities/general/clearfix, but that adds overflow: hidden to your container.
overflow: hidden is annoying since it prevents margins from collapsing. It also hides your overflow (duh!), cutting off box shadows from child elements.
The future
We might eventually get a standards clearfix with 
  display: flow-root
  
    Show archive.org snapshot
  
.