Let C be a curve of genus 2 over a finite field for which we want to find the number of points. This problem can be reduced to counting points on the Jacobian of C, which is easier, due to its group structure.

After recalling some basics about these objects, we will describe a Schoof-like algorithm which gives a solution to our problem in polynomial runtime and has been implemented in Magma.

Still, this algorithm is not yet enough to treat large examples and the natural question is how to extend to the genus 2 the methods of Elkies-Atkin which have proved to be efficient for elliptic curves. We will present a construction of some modular equations that can be useful in this context.