The Kepler-discovered Systems with Tightly-packed Inner Planets (STIPs), typically with several planets of Earth to super-Earth masses on well-aligned, sub-AU orbits may host the most common type of planets, including habitable planets, in the Galaxy. They pose a great challenge for planet formation theories, which fall into two broad classes: (1) formation further out followed by inward migration; (2) formation in situ, in the very inner regions of the protoplanetary disk. We review the pros and cons of these classes, before focusing on a new theory of sequential in situ formation from the inside-out via creation of successive gravitationally unstable rings fed from a continuous stream of small (~cm-m size) “pebbles,” drifting inward via gas drag. Pebbles first collect at the pressure trap associated with the transition from a magnetorotational instability (MRI)-inactive (“dead zone”) region to an inner, MRI-active zone. A pebble ring builds up that begins to dominate the local mass surface density of the disk and spawns a planet. The planet continues to grow, most likely by pebble accretion, until it becomes massive enough to isolate itself from the accretion flow via gap opening. This reduces the local gas density near the planet, leading to enhanced ionization and a retreat of the dead zone inner boundary. The process repeats with a new pebble ring gathering at the new pressure maximum associated with this boundary. We discuss the theory's predictions for planetary masses, relative mass scalings with orbital radius, and minimum orbital separations, and their comparison with observed systems. Finally, we discuss open questions, including potential causes of diversity of planetary system architectures, i.e., STIPs versus Solar System analogs.