This article describes the capture of heavy negative particles (µ − , π − , K − , p) by normal atoms, ions and molecules to form exotic systems. Capture by even the hydrogen atom presents great challenges for theoretical treatment. The wide variety of methods used are reviewed, including perturbative, two-state adiabatic and diabatic, time-independent quantum mechanical, timedependent semiclassical and quantum mechanical and quasi-classical treatments. A few of these methods, as well as the Fermi-Teller model, have also been applied to heavier atomic targets. Most of the methods, other than the quasi-classical formulations, are not yet up to treating the dynamical electron correlation and multiple ionization found to be important in capture by multi-electron atoms, or the vibronic coupling found to be important in capture by simple molecules. The essential elements of potentially more rigorous quantum mechanical theories are characterized. The experimental data on capture states and relative capture probabilities in mixtures are also discussed. The connection of this experimental data to the theoretical capture calculations is fairly tenuous, but forthcoming experiments with antiprotons promise direct tests of some of the recent theoretical findings.