Studies of charmless three-body decays of either B0(s) mesons or beauty baryons with a K0 meson in the final state are presented in this thesis. The analyses are performed using the 2011 and 2012 LHCb dataset, corresponding to an integrated luminosity of 1.0 fb−1 and 2.0 fb−1 recorded at a centre-of-mass energy of 7 TeV and 8 TeV, respectively. The decays B0s->K 0K±⇡⌥ and B0s -> K0⇡+⇡− are observed for the first time, and the decay mode B0 -> K 0K±⇡⌥, previously observed by the BaBar experiment, is confirmed. Moreover, the ⇤0b -> K0p⇡− channel is also observed for the first time and its phase-space integrated CP asymmetry measured, which shows no significant deviation from zero. No significant signals are seen for ⇤0b -> K0pK− decays, ⌅0 b decays to both the K0 S p⇡− and K0 SpK− final states, and the ⇤0b ! D−s (K0 SK−)p decay, and upper limits on their branching fractions are reported. Finally, the first untagged decay-time-integrated amplitude analysis of B0s -> K0 SK±⇡⌥ decays has been performed. All branching fraction results obtained from this analysis are either the most precise to date or are first measurements.