PS4 Remote Play with Xperia Z3 and MHL
I recently got a Sony Xperia Z3 Compact phone, which supports Remote Play with the PS4. Last night I picked up a MHL cable and hooked it up to my Dell U2414H monitor, allowing the monitor to mirror the phone's screen. Then I was able to use Remote Play on a 24-inch monitor!
MHL doesn't seem to be a really well-known standard. MHL enables a connection between a micro-USB port on your phone or tablet and an HDMI port on your monitor or television; the phone outputs video, while the monitor actually recharges the phone simultaneously. If your monitor's HDMI ports support the MHL standard (as is the case with the Dell U2414H), then all you need is a passive MHL cable; I picked up one from Fry's yesterday for $10. If your monitor doesn't support MHL, you'll need an active MHL adapter; this requires an extra USB connection for power.
MHL actually supports 7.1 sound, but my monitor only has a headphone jack for audio output, so I was limited to stereo. The video quality wasn't perfect, but I'm sure that's due to the Remote Play rather than the MHL. It's not the same as playing on my Pioneer plasma, but as a Remote Play setup, it's pretty nice.