Niantic's European Head of Product Marketing, Anne Beuttenmüller, announced in an interview with Gram magazine that PvP will be coming to Pokemon Go by the end of this year.
Beuttenmüller doesn't go into much detail about how the PvP will play but we can assume it'll work similarly to gym battles. You attack your opponent's Pokemon by tapping and avoid their attacks by swiping.
The interview happened during a Cassandra Prime event that was held on July 27th - 29th in Warsaw, Poland. Cassandra Prime events tie into Niantic's other big game, Ingress, which is a similar location-based AR game.
Pokemon Go seems to have really bounced back in a major way since the drought it experienced a few months after it was released. The vast improvements Niantic have made to the game haven't gone unnoticed and people are starting to hop back in to catch em' all.
Niantic probably want to get PvP out by the end of the year to coincide with the release of Pokemon: Let's Go which is coming out November 16th. We have a preview of the game up right now that you should read to see how Pokemon Go has influenced the gameplay of Let's Go.