Digital connectivity has become the foundation of prosperity and an essential need for functioning societies. Despite this dependence, limitation on Internet access remains a prevalent issue, largely hinged on socioeconomic and geographic factors. A promising solution to attain global access equality is based on integrated terrestrial-satellite networks that rely on low Earth orbit (LEO) mega constellations. While the benefits of LEO constellations complement the shortcomings of terrestrial networks, their incorporation impacts the network design, adding complexity and challenges. This article presents a systematic analysis of next generation LEO mega satellite constellations and outlines opportunities by virtue of the many benefits these constellations can provide and highlights the major challenges. Furthermore, it provides a synopsis of analytic models and underscores modern simulation approaches for next generation mega satellite constellations. This provides network designers with the necessary insights into satellite network performance.