We prove a new lower bound on the Ramsey number r(ℓ, Cℓ) for any constant C > 1 and sufficiently large ℓ, showing that there exists ε(C) > 0 such that r(ℓ, Cℓ)( p_C^−1/2+ ε(C) )^ℓ, where p_Cdenotes the unique solution in (0, 1/2) satisfying C = log p_C/ log (1 − p_C). This provides the first exponential improvement over the classical lower bound by Erdős since 1947. We will also aim to discuss some recent development related to this approach. Joint work with Wujie Shen and Shengjie Xie.