In this talk, we will introduce three finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes for hyperbolic conservation laws, where the solution and its derivatives are both involved in time. The common idea of the three HWENO schemes is to restrict the derivatives by a high order HWENO limiter, as the derivatives would become quite large near discontinuities, and the HWENO limiter can well maintain the fifth order accuracy and control spurious oscillation simultaneously. Compared with the original finite difference HWENO scheme of Liu and Qiu (J. Sci. Comput., 63:548-572, 2015), the three schemes can use a larger CFL number and achieve higher order numerical accuracy for two-dimensional problems. Furthermore, the latest of the three schemes is very robust for some extreme problems, even without positivity-preserving limiters. In addition, the three schemes preserve the nice property of compactness shared by HWENO schemes, i.e., only immediate neighbor information is needed in the reconstruction, and they have smaller numerical errors and higher resolution than fifth order WENO schemes with the same reconstructed technique. Extensive numerical tests are performed to demonstrate the fifth order accuracy, efficiency, robustness, and high resolution of the proposed HWENO schemes.