Abstract-Power systems have typically been designed to be reliable to expected, low-impact high-frequency outages. In contrast, extreme events, driven for instance by extreme weather and natural disasters, happen with low-probability, but can have a high impact. The need for power systems, possibly the most critical infrastructures in the world, to become resilient to such events is becoming compelling. However, there is still little clarity as to this relatively new concept. On these premises, this paper provides an introduction to the fundamental concepts of power systems resilience and to the use of hardening and smart operational strategies to improve it. More specifically, first the resilience trapezoid is introduced as visual tool to reflect the behavior of a power system during a catastrophic event. Building on this, the key resilience features that a power system should boast are then defined, along with a discussion on different possible hardening and smart, operational resilience enhancement strategies. Further, the so-called ΦΛΕΠ resilience assessment framework is presented, which includes a set of resilience metrics capable of modelling and quantifying the resilience performance of a power system subject to catastrophic events. A case study application with a 29-bus test version of the Great Britain transmission network is carried out to investigate the impacts of extreme windstorms. The effects of different hardening and smart resilience enhancement strategies are also explored, thus demonstrating the practicality of the different concepts presented. However, ensuring an uninterrupted electricity supply is challenging, as power systems are exposed to several threats. These threats can be mainly categorized in typical power system outages and extreme events, driven for instance by natural disasters/extreme weather. There are distinct differences between these two categories, as shown in Table I [4]. Hence, electrical power systems have been designed in a way that they possess high levels of reliability to the more typical threats. Latest events are now creating compelling cases for power systems to also boast high levels of resilience to natural disasters and extreme weather, to reduce the frequency and severity of power disruptions. Power systems reliability is a well-known and established concept, and several reliability-oriented studies have been developed by power system engineers and scholars. In contrast, there is much less clarity as to the concept of resilience. "Resilience" originates from the Latin word "resilio" and, having been first introduced by C.S. Holling in 1973 for ecological systems [5], is a relatively new and emerging concept in the area of power systems. Within this context, power systems resilience can be referred to as the ability of a power system to recover quickly following a disaster or, more generally, to the ability of anticipating extraordinary and high-impact, low-probability events, rapidly recovering from these disruptive events, and absorbing lessons for adapting ...