abstract: Understanding the entanglement properties of systems with many degrees of freedom, such as quantum spin chains, has been one of the main recent research topics connecting quantum information science and statistical physics. Huge amount of results has been accumulated about translation-invariant systems. However, the results almost exclusively correspond to models with reflection symmetry, despite that non-reflection-invariant systems also play a prominent role in statistical mechanics (e.g. in describing non-equilibrium steady states, or in case of spin models with Dzyaloshinskii-Moriya interactions). In this talk we will present some new results, both analytical and numerical, about the entanglement properties of non-reflection-invariant spin chains, and discuss how these differ from the reflection-invariant case.