JavaScript security question

Example - Let's say you have 2 text boxes, both are for user input.

The user types in whatever they want into those two text boxes and clicks a button, the button then uses a bit of javascript, concatenates whatever is in those two text boxes and displays it out in a div.

My question is, in this case, since it's using javascript client side, do you need to really sanitize user input?

What if it outputted to another text box? or What if it outputted as an 'alert'?

I understand that when it comes to forms/PHP you always want to sanitize input, but I'm not really familiar with java script security precautions.