There's a few authors who carried on the Lovecraftian tradition - August Derleth, Clark Aston Smith, Robert Bloch (although his most notable work is not Lovcraftian - he wrote the book Psycho, later filmed by Hitchcock). Later on Ramsey Campbell and Brian Lumley.

Then there's the kind of post-Lovcraftian stuff - Thomas Ligotti is the big name in that area.

There's also a few modern authors who tried to bring modern sensibilities to Lovecraft's work. Ruthanna Emrys' re-imagining of the Innsmouth based events for example.