Linear systems of equations can be either solved with direct methods as the LU-decomposition or with iterative methods. These iterative methods are the Gauss-Seidel method, successive over-relaxation, the Jacobi method, and others.
Iterative methods are computationally less demanding as they only require matrix-vector multiplications. However, using an iterative approach may not work when the chosen method does not converge, or the convergence may be slow.
On the other hand, the direct approach is easy as one gets the exact solution without taking care of convergence and precision.
So, what are the applications for which we prefer iterative methods over direct methods?
Edit: As noted in the comments, iterative methods may be used for large systems of equations where the precision of the solution is not that important. However, I still wonder in which applications do we have these conditions.