In Bayesian multi-object filtering, in contrast to Bayesian single object filtering, the number and the individual states of objects are to be determined in the presence noise, detection uncertainty and false alarms. The Randon Finite Set (RFS) or Finite Set Statistics (FISST) approach is a rigorous and systematic framework for estimation in multi-object systems. The centrepiece of this framework is the so called Bayes multi-object filter, a theoretically sound yet computationally challenging recursion, which propagates the multi-object posterior density. Well known and tractable yet efficient recursive solutions for multi-object estimation, based on approximations of the Bayes multi-object filter, currently exist via moments and parameterizations. This paper summarizes new results which present a conjugate or exact closed form solution to the Bayes multi-object filter.