The quartic Higgs self-coupling is the final measurement in the Higgs potential needed to fully understand electroweak symmetry breaking. None of the present or future colliders are known to be able to determine this parameter. We study the chances of measuring the quartic self-coupling at hadron colliders in general and at the VLHC in particular. We find the prospects challenging.The LHC and a future linear collider are widely regarded as an ideal combination of experiments to understand electroweak symmetry breaking, i.e. study the Higgs boson and measure its couplings to all Standard Model bosons and fermions. According to the electroweak precision data [1] we expect to discover and identify a light Standard Model Higgs boson at the LHC [2,3,4]. At the ILC we will be able to measure Higgs couplings to all Standard Model particles with great precision [5]. 1 A particularly exciting task is the measurement of the trilinear Higgs self-coupling: for a Standard Model Higgs boson heavier than 150 GeV this coupling can be measured at a luminosity-upgraded LHC (but not at the ILC) [7,8,9]. In contrast, for small Higgs masses around 120 GeV it can be measured at the ILC (but possibly not at the LHC) [10,11,12].Higgs potential at Colliders: The measurement of the Higgs self-coupling is crucial to determine the Higgs potential -the way we think the electroweak symmetry is broken. A general parameterization of the Higgs potential with one doublet Φ (as in the Standard Model) is [13]:where v = ( √ 2G F ) −1/2 is the vacuum expectation value, and G F is the Fermi constant. In the Standard Model,If we consider the Standard Model an effective theory, λ 0 stands for two otherwise free parameters, namely the trilinear and the quartic scalar self couplings. An upper limit can be determined using unitarity arguments, assuming the model's validity to high energy scales [14]. In the Standard Model, the two self-couplings are linked as the leading terms in eq.(1), namely λ 3 /λ 4 = v, and higher dimension operators are not expected to appear much below the Planck scale. If we allow for an intermediate scale Λ ≪ M Planck and include the higher dimensional terms n = 1, 2 both self couplings receive different corrections:In general, it is not even guaranteed that both self-couplings have to be positive, since the stability of the general Higgs potential is guaranteed by the sign of the highest power in the Higgs field alone.The relation between the Higgs mass and each self-coupling as well as between the two self-couplings can change dramatically when we move to the MSSM with its two Higgs doublets. If we replace the Standard Model Higgs with the light CP-even scalar h 0 the relation between the self coupling becomes λ 3h /λ 4h = v sin(β + α)/ cos 2α [15]. As usual, tan β is the ratio of the two vacuum expectation values and α is the mixing angle between the two Higgs scalars. However, if we assume a mass hierarchy between the light Higgs scalar and the remaining Higgs sector the difference to a Standard-Model like Higgs is very small.