Classical regularity theory for nonlocal integro-differential operators typically relies on a fixed, strictly positive order of differentiability. When this order becomes very small or approaches zero—the low-order regime—traditional fractional Sobolev spaces lose their embedding properties, and standard analytical techniques break down. This talk explores the surprising regularizing effects that still occur at this critical threshold. Aiming at minimal assumptions on the underlying kernel, we will discuss recent progress on the interior behavior of weak solutions, highlighting how structural properties of the kernels can restore smoothness, boundedness, and continuity even under highly anisotropic or nearly zero-order conditions.