Is what we have now what they wrote then?

Excellent lecture by Dan Wallace from the Center for the Study of New Testament Manuscripts (CSNTM for a much needed abbreviation). He knows what he's talking about, as can be evidenced by his bold and confident choices of shirts.

Here's a good article on the issue 

and another

and another

Here is an article with the six step mnemonic device on how we know we can trust the Bible is accurate and authoritative.