This paper addresses the problem of efficiently virtualizing NUMA architectures. The major challenge comes from the fact that the hypervisor regularly reconfigures the placement of a virtual machine (VM) over the NUMA topology. However, neither guest operating systems (OSes) nor system runtime libraries (e.g., Hotspot) are designed to consider NUMA topology changes at runtime, leading end user applications to unpredictable performance. This paper presents eXtended Para-Virtualization (XPV), a new principle to efficiently virtualize a NUMA architecture. XPV consists in revisiting the interface between the hypervisor and the guest OS, and between the guest OS and system runtime libraries (SRL) so that they can dynamically take into account NUMA topology changes. The paper presents a methodology for systematically adapting legacy hypervisors, OSes, and SRLs. We have Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. applied our approach with less than 2k line of codes in two legacy hypervisors (Xen and KVM), two legacy guest OSes (Linux and FreeBSD), and three legacy SRLs (Hotspot, TCMalloc, and jemalloc). The evaluation results showed that XPV outperforms all existing solutions by up to 304%.