In this talk, we classify simple restricted modules over the mirror Heisenberg-Virasoro algebra and the twisted Heisenberg-Virasoro algebra with nonzero level. This is much more challenging in contrast to the case of zero level. We introduce the Frenkel-Lepowsky-Meurman operators on restricted modules over the Heisenberg algebra, and develop new techniques. As applications, we characterize simple Whittaker modules and simple highest weight modules. A vertex-algebraic interpretation of our result is the classification of simple weak twisted and untwisted modules over the Heisenberg-Virasoro vertex algebras. This is a joint work with Haijun Tan and Kaiming Zhao.