Thousands of exoplanets have been discovered in the past ~30 years. Kepler has shown us close-in sub-Neptune exoplanets (<1AU, <4R_earth) are extremely common in our Galaxy but somehow absent in our solar system. The James Webb Space Telescope is poised to characterize some of these planets in detail. With LUVOIR/HabEx and GMT/TMT recommended by the NASA 2020 Decadal Survey, the detection of biosignatures, the holy grail of the exoplanet community, may be just a few decades ahead of us. However, there are still major gaps of knowledge in our understanding of planet formation, evolution, and habitability. The most extreme exoplanets are ideal for identifying, isolating, and investigating the open questions. In this talk, I will highlight three archetypal extreme planetary systems: 1) the ultra-short-period planets (<1 day, <2 R_earth) will help understand the composition, surface mineralogy, and formation pathways of terrestrial planets.  2) The young “super-puffs” (planets with anomalously low density <0.1 g cm^-3; ~100-Myr-old) are experiencing intensive hydrodynamical atmospheric erosion: a regime of mass loss that is not observed on any current-epoch solar system planets. 3) I will showcase a multi-planet system with all six planets locked deep in a chain of mean-motion resonances. This resonant system is likely a fossil record of the initial orbital architecture produced by convergent disk migration.