Go for a long walk in the park? All that time your phone's wifi is straining to find a wifi signal. It's not as big a power sap as the screen, however it's constantly, silently in use and the screen isn't.
If you are on Android, my guess is that your phone was set to be connected to Wifi during sleep. You can control it by going to Wifi networks section -> menu -> Advanced -> Keep Wi-Fi on during sleep, then setting it to "Only when plugged in" or "Never".
If you're driving around with the phone set to leave the Wifi on during sleep, it'll be constantly going in and out of range of various Wifi connections. If the Wifi part is set for passive scan, then the processor needs to be kept up as the Wifi chip attempts to collect the BSSID of all the network it see and processor tries to figure out whether these networks have been seen or not. If it's set for active scan, then the Wifi needs to power up the radios to transmit beacons. Pretty bad news in either case, unfortunately.
Llama by itself uses less battery than leaving the wifi chip on, even in passive scanning mode, as the phone is always looking and checking cell towers.
It doesn't make unicorns shit rainbows or defy the laws of physics.
I've seen apps do some crazy things and it really has a significant effect in over-all battery life. A popular Android weather clock widget woke the phone up every minute to update the minute number on the graphics and updated the weather information every ~15 minutes (gps + radio!) which single handily crushed the standby battery life from multiple days to less than 8 hours.
Yes, I don't think _every_ decision should be based on minimizing the wake ups... but on the other hand, all developers should at least try to have as much understanding of the platforms that they're working on so that they know what trade-offs they're making with each feature they're adding.
I'm glad that Google has these videos available and that they're being picked up in places like HN.