We present a review of electron detachment cross sections of atomic, molecular, and cluster anionic projectiles colliding with atoms and molecules, the main focus being on reporting systematic experimental studies. These studies use an experimental method developed at our laboratory, which uses the gas cell of standard tandem accelerators as a collision target. The experimental data show that the velocity dependence of electron detachment cross sections can be described modeling negative ions as a quasi-free electron bound to a neutral core. Using this model, a velocityindependent contribution to cross sections is associated with the neutral projectile core, while a velocity-dependent curve is associated to the projectile quasi-free electron. This latter curve is the convolution of experimental free-electron cross sections, for the same target, with the momentum distribution of the quasi-free projectile electron. This model is useful to obtain cross section estimates, as exemplified by its application in several collision systems relevant for inertial fusion and plasma diagnostics. It is also a powerful tool for verifying the accuracy of anion structure calculations.