The iron-based superconductors display rich phase diagrams featuring various types of electronic order, such as antiferromagnetism, electronic nematicity, and superconductivity. The proximity between the antiferromagnetic and superconducting instabilities has motivated the idea that magnetic correlations promote the pairing interaction, although the precise mechanism remains under debate. Importantly, different antiferromagnetic ground states are realized, from the widely observed stripe spin density-wave phase to the more recently discovered spin-vortex crystal and charge-spin density-wave phases. Interestingly, each of these magnetic ground states is intertwined with a different type of composite order – nematic order, spin-current order, and checkerboard charge order, respectively – which can onset even before the emergence of long-range magnetic order as vestigial phases. In this talk, we will discuss unique effects that arise from the interplay of these intertwined orders with lattice disorder and topological phenomena. In the first part, we will present our results for the impact of lattice disorder on the intertwined stripe antiferromagnetic and nematic orders. In particular, we will show that lattice defects that are ubiquitously present in the surface of a crystal stabilize a novel electronic smectic phase. We will also demonstrate that random strain created by lattice defects in the bulk of the crystal generates new correlations between the magnetic degrees of freedom, which are not captured by the usual random-field Ising-model physics. In the second part, we will discuss how the vestigial phase of the spin-vortex crystal can host topological Weyl points in the presence of an externally applied magnetic field, due to its breaking of the inversion symmetry with respect to the Fe plane. Finally, we will discuss possible experimental manifestations of the phenomena presented in this talk in different iron-based compounds, such as BaFe₂As₂, FeSe and CaKFe₄As₄.