Fields not transferring after Conversion.

When I am converting leads to contacts, it is not transferring all of the information to the contact card. Why is this happening and how can I get around it? For example, I just put a lead in this morning, filled out all his information with address, phone number, all the custom fields I created for our business, and the ONLY things that transferred to his contact card was Name, phone number and email address. Now all of his other information is gone. What am I doing wrong here? This is hugely frustrating, and if it is designed to be like this, I think it is a HUGE shortfall.

Looking for some answers.

Thanks,