Two polymorphs of the borosulfate Cu[B2(SO4)4] can be selectively prepared by solvothermal syntheses. The crystal structures of inosilicate-analogous α-Cu[B2(SO4)4] (P1̄, no. 2, a = 5.2636(2), b = 7.1449(2), c = 7.9352(2) Å, α = 73.698(2)°, β = 70.737(2)°, γ = 86.677(2)°, 65 parameters, RBragg = 0.0052) and the new phyllosilicate-analogous polymorph β-Cu[B2(SO4)4] (P21/n, no. 14, a = 7.712(3), b = 8.149(3), c = 9.092(3) Å, β = 111.22(1)°, 3829 independent reflections, 106 parameters, wR2 = 0.054) are discussed. Further, the optical, magnetic and thermal properties of both polymorphs are investigated with focus on the role of the Cu2+ cation and its Jahn-Teller effect. The findings are confirmed by DFT calculations yielding insights in the stability of the synthesised polymorphs as well as a predicted γ-modification. Additionally, the crystal structures of two polymorphs of copper hydrogensulfate Cu(HSO4)2-I (P21/n, no. 14, a = 4.7530(2), b = 8.5325(4), c = 7.3719(3) Å, β = 100.063(1)°, 1063 independent reflections, 55 parameters, wR2 = 0.052) and Cu(HSO4)2-II (P1̄, no. 2, a = 4.79.88(8), b = 7.857(1), c = 8.057(1) Å, α = 77.86(1)°, β = 87.02(1)°, γ = 89.82(1)°, 1044 independent reflections, 109 parameters, wR2 = 0.132) as well as that of Cu[S2O7] (C2/c, no. 15, a = 6.6341(4), b = 8.7302(5), c = 9.0555(8) Å, β = 104.763(3)°, 1117 independent reflections, 48 parameters, wR2 = 0.049) are presented and the cyclosilicate-analogous borosulfate Cu[B(SO4)2(HSO4)] is fully characterised with respect to its optical and thermal properties.