Whereas lot of nice results are known for small rank groups, like GL(2), almost nothing is known for, say, Siegel or Jacobi modular forms of higher degrees. In this talk we aim to discuss some conjectures and results in this area. We use either the theory of Poincare series or averages of central values of L-functions to tackle this problem. Our methods have the benefit of having a hands-on approach and fits into many situations.