We present results for the triplet distribution function g(3)(r,s,t) of hard-spheres obtained in extensive molecular-dynamics simulations; the packing fractions we have investigated range from 0. 15 to 0.45. The simulation data have been compared to results for g(3) (r,s,t) which we calculated via some recently proposed analytical and numerical methods; two of these methods are based on density-functional theory and the Wertheim-Thiele solution of the Percus-Yevick equation; another method, proposed by Barrat, Hansen, and Pastore uses a factorization ansatz for the pair direct correlation function and the last approximation is based on a formal density expansion of g(3) (r,s,t), truncated after second order. Furthermore we compared, simulation results to data obtained by the "source-particle method" (or PY3 method) proposed a few years ago by Attard. Attard’s method shows an extremely good agreement not only for general configurations, but in particular for particles at direct contact; this approximation has to be considered as the most reliable method available for the numerical determination of the triplet-structure of a simple liquid. Concerning the results of the other methods discrepancies with the simulation data are observed in particular near the contact and for very close triplet-configurations. Apart from Attard’s approximation the second order density expansion gives the best agreement. For less close configurations, i.e., if particles are separated by 1.5 to 2 hard-sphere diameters, the results of all the methods investigated practically coincide.