Amending your returns is one thing. You can see how to do that in this Help Article.
Another issue is that you were incorrectly filing as single when you were married. When one is married the main two filing status options are: married filing jointly (MFJ) or married filing separately (MFS). Sometimes, if qualifying factors are met, one may file with a Head of Household status.
Another consideration is that if your spouse had income during those years but was not a US resident, filing MFJ will mean that the spouse will be considered a US resident and worldwide income declared on the US tax return and US taxes paid. Please read this article carefully to get a basic understanding of how this works.
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