In this talk, we will discuss the application of bound preserving flux limiters for high order methods solving scalar conservation laws. Traditionally, total variation diminishing stability is necessary for ensuring numerical solutions converge to weak solutions of the hyperbolic conservation laws. For first order schemes, total variation stability is well established, especially for monotone schemes, or E-Schemes in general. For high order methods, one can only rely on total variation bounded stability in spirit. Examples include the ENO and WENO methods, high order discontinuous Galerkin methods with TVB limiters. This family of approaches are total-variation stable and useful in practice, in the sense that numerical results do not show visible oscillations. The issue is that total variation bounded stability is not mathematically justifiable, even though it is validated through extensive numerical experiments. Therefore, the focus of this talk is on designing high order methods with inherent, mathematically proven total variation stability.