Saint-Venant system of shallow water equations and related models are widely used in many scientific applications related to modeling of water flows in rivers, lakes and coastal areas. The development of robust and accurate numerical methods for the computation of the solutions to shallow water models is an important and challenging problem. The Saint-Venant system is a hyperbolic system of balance laws. A good numerical method for the Saint-Venant system has to preserve a delicate balance between the flux and the source terms (in other words, the scheme must be well-balanced) to prevent the formation of the “numerical storm” - when artificial numerical waves have a larger magnitude than the actual water waves to be captured. It is also crucial to develop a positivity preserving scheme that can approximate dry/almost dry areas without producing negative water depth. Moreover, many engineering applications have to deal with models in domains with complex geometry, and the design of an accurate numerical scheme becomes an even more difficult task in this case. In the talk, we will introduce and discuss a simple second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. In our talk we will show that the developed scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We will demonstrate these features of the scheme, as well as its high resolution and robustness in a number of numerical examples. Current research and future directions will be discussed as well. This is a joint work with Jason Albright, Steve Bryson, Alexander Kurganov and Guergana Petrova.