In this work studies have been carried out into the structures of three families of layered perovskite using powder neutron diffraction. It is shown that Bi₅Ti₃FeO₁₅ exhibits only one high temperature phase transition, from A2₁am to I4/mmm. For another 4-layer Aurivillius phase, BaBi₄Ti₄O₁₅, the room temperature structure has been successfully refined in space group F2mm. Both of these results are in contradiction to earlier suggestions. La³+ doping into 2- and 3-layer structures was investigated in Bi₃₋ₓLaₓTiNbO₉ for 0 ≤ x ≤1 and Bi₄₋ₓLaₓTi₃O₁₂ for 0 ≤ x ≤ 2. The transition from polar to centrosymmetric has been examined and is in agreement with documented ferroelectric properties. The series Bi₂Sr₂2Ti₁₋ₓGaₓNb₂O₁₂₋ₓ/₂ and BaBi₄Ti₄₋ₓGaₓO₁₅₋ₓ/₂ were studied for x = 0.2, 0.5 and 1 using powder X-ray diffraction. The presence of a second phase, Bi₂O₃ was identified. The presence of this impurity would suggest that the main phases are unlikely to be oxide ion conductors, as previously suggested. The structures of the 2-layer Dion-Jacobson phases CsBiNb₂O₇ and CsNdNb₂O₇ and the 4-layer CsBi₃Ti₄O₁₃ have been determined using space group P2₁am. The system of octahedral tilting within the perovskite blocks is analogous to that observed in the ferroelectric Aurivillius phases, though no ferroelectric behaviour has been observed. Contrasting behaviour has been found in the 3-layer phases CsA₂Ti₂NbO₁₀ (A = La, Nd, Bi), with the Nd and Bi phases adopting an orthorhombically distorted version (space group I2cm) of the parent tetragonal structure of the La derivative. Atomistic calculations have been used to study the possibility of doping Me3+ (Me = Al, Ga, In) into BaBi₄Ti₄O₁₅ and BiTi₄O₁₂; these suggest the doping of In3+ into the [Bi₂O₂] layer as the most energetically favoured. The O position in the [Bi₂O₂] layer was given as the lowest energy site for oxygen vacancies, however, the possibility of oxygen migration in Bi₄Ti₃O₁₂ was found to be unfavourable. At the dilute limit La3+ doping was suggested to occur at the [Bi₂O₂] layer in Bi₄Ti₃ O₁₂.