<p>The hint of a pseudoscalar toponium state at the Large Hadron Collider (LHC) opens a new avenue for studying a novel class of QCD (quasi-)bound states with comparable formation and decay times. Compared with charmonium and bottomonium, toponium is a quasi-bound state, resembling a hydrogen atom of the strong interaction, although it appears as a broader resonance. We compute the masses and annihilation decay widths of the lowest <i>S</i>-wave (<i>η</i>_<i>t</i>, <i>ψ</i>_<i>t</i>) and <i>P</i>-wave (<i>χ</i>_<i>t</i>0, <i>χ</i>_<i>t</i>1) toponium states, and assess their discovery prospects at the High-Luminosity LHC (HL-LHC) and future lepton colliders, such as the <i>e</i>⁺<i>e</i>^<i>−</i> stage of the Future Circular Collider (FCC-ee). Detecting the vector <i>ψ</i>_<i>t</i> state at the HL-LHC is hindered by the Landau-Yang theorem and the gluon-dominated production environment of the collider, whereas lepton colliders offer promising sensitivity through both constituent and two-body decays. A more precise measurement of the <i>η</i>_<i>t</i> mass-approximately equal to that of <i>ψ</i>_<i>t</i>-at the LHC could help determine the optimal <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( t\overline{t} \)</EquationSource> </InlineEquation> threshold center-of-mass energy for FCC-ee. The <i>P</i>-wave states remain challenging to observe at both the HL-LHC and future lepton colliders. We also discuss how toponium measurements can be used to probe top-quark properties and to conduct indirect searches for new physics, including light scalars that couple to the top quark.</p>