In this work we have performed Laser Photodetachment Threshold Spectroscopy (LPTS) to determine the electron affinities of the atomic species $^{133}$Cs and $^{16}$O with high precision. The negative ion of Cesium has been produced and investigated at the Gothenburg University Negative Ion and Laser LAboratory (GUNILLA) while the Oxygen anion have been studied in the Double ElectroStatic Ion Ring ExpEriment (DESIREE) at Stockholm University. Pilot studies have also been carried out to measure the electron affinity of complex molecular systems in DESIREE. Specifically, we have studied the beautifully symmetric fullerene C$_{60}^-$ negative ion and its spontaneous and laser induced decays. A preliminary analysis suggests that DESIREE's internal temperature of $\unit{13}{\kelvin}$ may allow an efficient cooling of these initially created hot molecules on time scales of a few seconds. This is a key aspect in measuring detachment thresholds as cooling suppresses hot band contributions associated with vibrationally excited states. Therefore, photodetachment techniques of the types successfully used for atomic species can be implemented for molecules. The preliminary results appear to settle a matter of disagreement in the literature concerning the most precise method to measure the EA of C$_{60}$, that is, LPTS or Photodetachment Electron Spectroscopy (PES).