After installing OS X 10.10.3, you will find your Mac undergo the standard restart that is part of the update process, but then see it hang up as OS X loads, leaving you with a gray screen. This is likely happening because because of some changes made to Apple’s FileVault full disk encryption routine.

Along with the 10.10.3 update, Apple issued an update for the OS X Recovery system in Yosemite, which will adjust some of the contents of the hidden recovery partition. This partition is used for unlocking your boot drive at startup, and it appears a problem with the update for some people has caused the drive to improperly unlock the drive.

If this is happening to you, then your drive and its contents should be safe, and while you can format your system and restore from a backup (that you hopefully made before updating), you can likely fix the problem by disabling FileVault.

Even though the system cannot boot to the main boot drive, it should still be able to boot into Recovery Mode, so do this by restarting and then holding the Command-R keys at startup (or the Option-Command-R keys). When in Recovery Mode, perform the following steps:

1. Open Disk Utility
2. Select your boot drive in Disk Utility’s sidebar
3. Click the toolbar option to unlock the drive
4. Select “Turn Off Encryption” from the File menu

After confirming you wish to disable encryption, choose Startup Disk from the Apple menu, and then re-select your boot drive, followed by restarting your system. This will bypass FileVault and should boot your system properly, though it may take a few minutes longer to boot. When loaded, you can re-enable FileVault in the Security system preferences.

While you might see this frustration as reason to keep FileVault disabled, do not allow it to dissuade you from using the technology, especially if you are concerned about theft and data privacy. FileVault will keep all of your data as secure as possible, but as with any encryption, if a problem does occur then you can lose your data, so the protection for this is to have redundant backups (a good practice even without using any encryption).

You can do this with Apple’s Time Machine, or a number of third-party tools, and also ensure the backup drive is encrypted. Then simply keep these backups updated, especially before applying any software updates or other system changes. By doing so you should be able to recover from almost any problem you encounter.