One weakness that Siri has is its lack of compatibility with third-party apps (though Apple is working on it). For instance, if you ask Siri to play music on Spotify, she'll tell you point-blank that she can't do it. While you can pause and skip Spotify tracks using Siri, there's not much else you can do — but Spotify has its own voice assistant to fill the gap.
In a recent update to the Spotify Music app for iPhone, Spotify has added the ability to use voice commands to control its entire library — from playing songs and albums to playlists and radio stations. They're calling it Spotify Voice. While you do need to be inside the app to perform these actions (unlike Siri, who you can call upon from anywhere), it's a very nice addition until Siri gets its act together.
When you first open up Spotify, you'll find yourself on the "Home" screen (the leftmost tab along the bottom). Just tap the "Search" tab (the magnifying glass), then you should see a microphone in the bottom-right corner. Tap that, hit "Get Started" to begin the process of using Spotify Voice, and tap "OK" to give Spotify access to your microphone when prompted.
After that, all you have to do is either tap the mic icon on the "Search" page or just long-press the "Search" tab to trigger Spotify Voice. A screen will pop up that says "What can I play for you?" At this point, you can ask it to play any artist, song, album, genre, radio station, or playlist on Spotify, and it'll play it as long as it understands you. Keep in mind that the music needs to be on Spotify for this to work.
Of course, it'd be great if Siri were able to integrate this function, but that likely won't be happening anytime soon. For now, though, this is a great stopgap.