Yes, since the demise of Doma - The defense of Marriage Act.
A K1 Visa is obtained in the country of origin and not the US. This involves application, evidence of your relationship (being real), a medical examination and an interview at the Consulate (again in the country of origin).
Once you have been approved, you must marry within 90 days of your arrival in the US.
After you are married, you must then apply for permanent residence which is conditional and lasts for 2 years. While your application is being processed you can also apply for work authorization and advanced parole which will allow you to work and travel while your green card application is being processed. You may or may not be required to attend an interview. There are certain triggers that may in the eyes of USCIS warrant an interview including large age gaps between spouses. Expect this to take between 6 and 9 months.
And once you get through all that, when your conditional residence is about 3 months away from expiring, you start the next round with USCIS. You need to get the conditions removed from your green card (its called an I751), which in effect will give you a 10 year green card ... but it takes an average of 15 months and a lot of stress.
You can do all of this on your own, and there are a lot of fees involved. We opted not to and hire a lawyer, since we decided it was too important for us to risk making mistakes. Total costs to date, are about 12K including all government fees.
There are many resources out there on the web offering support and advice but it is really important that you are very careful. I personally recommend getting a lawyer but it you cannot, be very careful with your paper work and triple quadruple check everything.
Hope this helps someone at some point