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Over the last week the Debian kernel team has worked to mitigate Meltdown in all suites. This mitigation is currently limited to kernels running in 64-bit mode (amd64 architecture), but the issue affects 32-bit mode as well.
You can see where this mitigation is applied on the security tracker. As of today, wheezy, jessie, jessie-backports, stretch and unstable/sid are fixed while stretch-backports, testing/buster and experimental are not.
Spectre needs to be mitigated in the kernel, browsers, and potentially other software. Currently the kernel changes to mitigate it are still under discussion upstream. Mozilla has started mitigating Spectre in Firefox and some of these changes are now in Debian unstable (version 57.0.4-1). Chromium has also started mitigating Spectre but no such changes have landed in Debian yet.