This paper investigates the jamming behavior of 2D and 3D systems with particles interacting via finite-range, repulsive potentials at zero temperature and zero applied stress. At low packing fractions, the system is not jammed, and particles can move freely. However, each configuration has a unique jamming threshold, φc, where particles can no longer avoid each other, and the bulk and shear moduli become non-zero. As the system size increases, the distribution of φc values becomes narrower, indicating that all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. The jamming threshold, Point J, occurs at zero temperature and zero applied stress and at the random close-packing density. It has properties reminiscent of an ordinary critical point, with power-law scaling for the divergence of the first peak in the pair correlation function and the vanishing of pressure, shear modulus, and excess number of overlapping neighbors. Near Point J, certain quantities no longer self-average, suggesting a diverging length scale. However, Point J differs from an ordinary critical point in that the scaling exponents do not depend on dimension but do depend on the inter-particle potential. As Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. At Point J, the density of states is constant down to zero frequency. These results suggest that Point J may control behavior in its vicinity, possibly even at the glass transition. The paper also discusses the concept of a "jamming phase diagram," which ties together different routes to kinetic arrest. Point J is shown to be an isostatic point, where the number of contacts equals the number of force balance equations. The paper concludes that Point J is a well-defined point in the jamming phase diagram and is the onset of jamming for a given initial state.This paper investigates the jamming behavior of 2D and 3D systems with particles interacting via finite-range, repulsive potentials at zero temperature and zero applied stress. At low packing fractions, the system is not jammed, and particles can move freely. However, each configuration has a unique jamming threshold, φc, where particles can no longer avoid each other, and the bulk and shear moduli become non-zero. As the system size increases, the distribution of φc values becomes narrower, indicating that all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. The jamming threshold, Point J, occurs at zero temperature and zero applied stress and at the random close-packing density. It has properties reminiscent of an ordinary critical point, with power-law scaling for the divergence of the first peak in the pair correlation function and the vanishing of pressure, shear modulus, and excess number of overlapping neighbors. Near Point J, certain quantities no longer self-average, suggesting a diverging length scale. However, Point J differs from an ordinary critical point in that the scaling exponents do not depend on dimension but do depend on the inter-particle potential. As Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. At Point J, the density of states is constant down to zero frequency. These results suggest that Point J may control behavior in its vicinity, possibly even at the glass transition. The paper also discusses the concept of a "jamming phase diagram," which ties together different routes to kinetic arrest. Point J is shown to be an isostatic point, where the number of contacts equals the number of force balance equations. The paper concludes that Point J is a well-defined point in the jamming phase diagram and is the onset of jamming for a given initial state.