Yeah, CDs and DVDs are not 100% reliable - I would not have that as your only copy of images. They are easily scratched or damaged and you also get what's called "disc rot" where the material used in the disc to hold the data starts to degrade over time, thus rendering it unreadable by the drive.
External hard drives can be good - but they will also eventually fail, as will any electro-mechanical device. You should keep multiple copies of things you don't want to lose.
I have all my photos on a 2nd hard drive in my computer - takes about 3TB all up, but that includes quite a bit of video as well. I back this up to a file server I have in my office (you could back it up to any other computer you have, or use multiple external drives) and I also back it up using a cloud backup service.
I currently use CrashPlan, but they are discontinuing their personal backup service next year so I'd recommend
BackBlaze now ... US$5 per month for unlimited cloud backup.
Be aware that BackBlaze has an annoying thing where you can backup files on an external hard drive, but if you don't plug that drive in at least once a month, the files will be deleted from their servers after 30 days - it's the one thing they get the most complaints about.
Other cloud alternatives include Carbonite and iDrive, but they all have their quirks.