Are they primarily for listening to music while also blocking out noise

I mean yeah. I've also used just the noise cancellation for sleep in different environments, whilst whippersnipping etc. I'm referring to the over ears version here. I think as long as there's a Bluetooth connection active the noise cancellation will stay working until the battery dies. If the Bluetooth connection drops, the headphones turn themselves off by default after a while. There's a sony app that lets you change that though.