There is a long-established result in planetary dynamics that a small annular zone of coplanar orbits surrounding a planet’s orbit is a regime of strong orbital instabilities. This zone is variously called the planet’s chaotic zone or clearing zone or feeding zone. For a planet on a circular orbit, the width of this instability region is approximately a few times the planet’s Hill radius, ap(mp/3m*)1/3; another estimate of the width is 1.5ap(mp/m*)2/7. The latter estimate attributes the underlying mechanism for instability to dynamical chaos arising from the overlap of first order mean-motion resonances. The literature on the actual dynamical behavior of chaotic orbits in this zone is scarce. On long timescales, there are a few different statistically quantifiable outcomes for test particles in the chaotic zone of a planet. On short timescales, the evolution of chaotic zone orbits is particularly rich and it is relevant to the study of dynamic populations of small bodies in the Solar System, such as the Jupiter-family comets, the Centaurs and the scattered disk in the outer solar system, the near-Earth objects in the inner solar system, planetary ring-moon systems, interplanetary dust and exo-planetary debris disks. It is also of interest in astrodynamics for spacecraft-trajectory design. We will describe recent results of numerical investigations to better illustrate and understand these chaotic dynamics.