Meltdown and Spectre are entirely new classes of security vulnerability. Even with Intel doing all it can to get microcode and firmware updates out as quickly as possible, there are also changes that need to be made in motherboard vendors' UEFI code. Fortunately, it looks like Asus, Gigabyte, and MSI are on top of things—as long as you have a recent motherboard.
All three companies have lists available of motherboards that have or will soon be receiving security-related BIOS updates. Glancing over them, it looks like the big three of motherboards will be issuing updates for motherboards based on Intel's LGA 1151, LGA 2011v3, and LGA 2066 sockets. That means motherboards using 100-series, 200-series, 300-series, X299, and X99 chipsets.
It's possible that your particular motherboard is not being updated, even if it falls in the categories above. Check the listings for your specific model, and then check the BIOS version of the latest download to see if it matches. Not all of the updates are available, so if yours isn't you'll probably want to remain vigilant until it is. Intel says it is planning updates for every processor in the last five years, so hopefully updates for older motherboards will also be forthcoming from these companies.