We report the crystal structures of eight new synthetic multinary Rb-Cu sulfates representing four new structure types: δ-Rb₂Cu(SO₄)₂, γ-RbNaCu(SO₄)₂, γ-RbKCu(SO₄)₂, Rb₂Cu₂(SO₄)₃, Rb₂Cu₂(SO₄)₃(H₂O), β-Rb₂Cu(SO₄)Cl₂, β-Rb₄Cu₄O₂(SO₄)₄∙(Cu_0.83Rb_0.17Cl) and Rb₂Cu₅O(SO₄)₅. The determination of their crystal structures significantly expands the family of anhydrous copper sulfates. Some of the obtained anhydrous rubidium copper sulfates turned out to be isostructural to known compounds and minerals. Rb₂Cu₅O(SO₄)₅ is isostructural to cesiodymite, CsKCu₅O(SO₄)₅, and cryptochalcite, K₂Cu₅O(SO₄)₅. Rb₂Cu₂(SO₄)₃ also shows an example of crystallization in the already known structure type first observed for synthetic K₂Cu₂(SO₄)_3. “Hydrolangbeinite”, Rb₂Cu₂(SO₄)₃(H₂O), was formed as a result of a minor hydration of the initial mixture of reagents. The minerals and synthetic framework compounds of the A₂Cu(SO₄)₂ series demonstrate a vivid example of morphotropism with the formation of structural types depending on the size of the cations residing in the cavities of the [Cu(SO₄)₂]^2- open framework. To date, five types (α, β, γ, δ and ε) can be distinguished. We propose to call this series of compounds “saranchinaite-type”, since the stoichiometry A₂Cu(SO₄)₂ was first encountered during the discovery and description of saranchinaite, Na₂Cu(SO₄)₂. The discovery of β-Rb₂Cu(SO₄)Cl₂, a new monoclinic polymorph of chlorothionite, seems to be of particular interest considering the recently discovered interesting magnetic properties of synthetic K₂Cu(SO₄)X₂ (X = Cl, Br) and Na₂Cu(SO₄)Cl₂. In the determined new structural architectures, a number of features were revealed which were seldom observed before. The first is the bidentate coordination of the sulfate tetrahedron via edge-sharing with the Cu²⁺-centered coordination polyhedron. Until recently, such coordination was known only for the chlorothionite structure. The second is formation of “high-coordinated” CuO₇ polyhedra. The structures of the new compounds suggest that such coordination is not in fact so uncommon, at least among anhydrous alkali copper sulfates. All of the described features clearly indicate the importance of further systematic studies of anhydrous copper-sulfate systems. Their exploration, particularly of the new copper-oxide substructures with new coordination environments, is highly likely to lead to new potentially interesting magnetic properties due to unusual arrangements of magnetically active Cu²⁺ cations. In addition to experimental details on the synthesis of rubidium analogs of anhydrous potassium and sodium sulfates, this work also provides an analysis and a brief review of the geochemistry of rubidium in volcanic environments.