A recent New York Times Magazine piece covers the evolution of machine learning methods for language translation.
If you're interested in building your own service that uses automatic translation then there are two big players in the space: Google and Microsoft. Both offer similar APIs although at slightly different price points and different technical limitations.
Microsoft's Translator API is free for the first 2,000,000 characters per month and then about $20 per month per 2,000,000 characters for extra use. Google's Translate API costs $20 per 1 million characters processed with no free tier (although I think you can use it for two months with a Google Cloud free trial).
Both services have limitations on the number of characters you can submit per document. Microsoft caps submissions at 10k characters and Google at 5k (although you could chunk the document yourself and push it through in pieces). They also both have attribution requirements if you are going to use their output in your product.
You can try Google Translate online for free: translate.google.ca. A few examples will show you that neither service will be replacing professional translators any time soon but you can get the gist of the text.