I uploaded a lead list that I had, I was wondering if there was a way where I can move the data around from one campaign to another one?

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You can do this two ways:

1. If you want to change the campaign for a single lead, simply edit that lead (go into the lead details by clicking on the name from the My Leads page). From the edit lead page, change the campaign to the desired one using the dropdown in the gray box in the Lead Information section, then save the lead.
2. If you want to change the campaign for many leads at once you can export those leads to a CSV, then delete them, then import them into the campaign you want.