<Badge badgeContent={4} primary={true}>
  <NotificationsIcon />
</Badge>

//override badgeStyle to account for padding of child element
<Badge badgeContent={10} secondary={true} badgeStyle={{top:12, right:12}}>
  <IconButton tooltip="Go To Cart">
    <ShoppingCartIcon/>
  </IconButton>
</Badge>

<Badge backgroundColor="#d8d8d8"
       badgeContent={<IconButton tooltip="Backup"><UploadIcon/></IconButton>}>
  <FolderIcon />
</Badge>

<Badge badgeContent="&copy;" badgeStyle={{fontSize:20}}>
  <h3>Company Name</h3>
</Badge>