Life on Other Worlds; How Might it Advance

When we look for life on other planets; what exactly are we looking for? Are we looking for similar life as we have found here on Earth or are we keeping our minds open to all the potential eventualities that might be? On Earth most of our life needs certain things, but is that because those certain things exist here already or because that is the only way life can exist? What if Earth had different components all around, what would life look like then? This is a fascinating subject and it recently came up in an online think tank when one member stated;