The problem of counting nodal curves on algebraic surfaces has been studied since the nineteenth century. On the projective
space $\mathbb{P}^2$, it asks how many curves defined by homogeneous degree $d$ polynomials have only nodes as
singularities and pass through points in general position. On K3 surfaces, the number of rational nodal curves was
predicted by the Yau-Zaslow formula.
G\"{o}ttsche conjectured that for sufficiently ample line bundles $L$ on algebraic surfaces, the numbers of nodal curves in
$|L|$ are given by universal polynomials in four topological numbers. Furthermore, based on the Yau-Zaslow formula he gave
a conjectural generating function in terms of quasi-modular forms. The formula is consistent with many existing results on
$\mathbb{P}^2$, K3, and curves with at most 8 nodes on general surfaces. In this talk, I will discuss how degeneration
methods can be applied to count nodal curves and sketch my proof of G\"{o}ttsche's conjecture.