What Loan Programs Are Available For Self Employed Mortgage Applicants?

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I'm looking to get my first home, a primary residence, but I am looking for solutions to overcome obstacles that I will face as a self employed applicant. I am looking for programs that require a low down payment and have low rates. I heard about 80/20 loans and 80/10/10 loans. Do these still exists? Is there other loan programs similar to these that I could take advantage of? 

My tax returns are an inaccurate reflection of my personal finances due to the amount of deductions I used. My bank statements and check receipts from clients serves as better indicators of my ability to pay a home loan. However, I read that they are hardly any loan programs that don't require at least 2 years of tax returns. Are there loan programs for self employed applicants that don't require tax transcripts?

What programs are available for self employed applicants? What do self employed mortgage applicants do to obtain financing?