Google has posted the factory images for the Nexus 4 and the Nexus 7 (2013). These images will updated those devices from Android 5.0 (build LRX22C) to Android 5.1 (build LMY47O).
For both devices, there is also the OTA update that has started to roll out these last days, but if you have not get the notification yet, now you can just flash the factory image.
Remember that when you flash an image on any previous version, they remove all your data by default, so be sure to have a backup of all your data before starting the process.
However, if you have an unlocked bootloader, you can remove the wipe command and keep your data on the device when updating to Android 5.1.
This is the full list of devices with factory image available at the moment:
Nexus 4 (LMY47O)
Nexus 5 (LMY47D)
Nexus 5 (LMY47I)
Nexus 6 (LMY47D)
Nexus 6 (LMY47E)
Nexus 6 (LMY47I)
Nexus 7 (2012) (LMY47D)
Nexus 7 (2012) Mobile (LMY47D)
Nexus 7 (2013) (LMY47O)
Nexus 7 (2013) LTE (LMY47O)
Nexus 10 (LMY47D)
With this last two files, all the nexus family have their corresponding Android 5.1 images, all but the Nexus 9. The newest Nexus tablet hasn’t the software ready yet, and there is no news regarding a possible schedule for the update.
You can download tall he factory images from Google, and you will also find there the instructions for a safe installation. If this is you first time flashing a factory image, read carefully all the steps and be sure you have a good backup of all your data before starting the process.