Topological phenomena embody a trendy, yet relevant, theme in modern condensed matter physics. Skyrmions, for instance, are robust ‘non-trivial’ spin textures, characterized by a winding number (‘topological invariant’), usually occurring in interacting electron systems, e.g., chiral magnets and fractional quantum Hall states. These topological entities are (purportedly) promising building blocks for the next generation of storage and information-processing media. In this talk I will show how the mesoscopic spin-orbit interaction present in ordinary non-topological and non-interacting electrons in GaAs wells can give rise to topological phenomena. More specifically, I will discuss (i) all- electron topological insulators and (ii) electronic Skyrmion lattice textures in double wells. I will also present the interesting possibility of devising stretchable ‘persistent spin helices’, i.e., robust non-interacting spin-density- wave-like excitations with variable pitches, thus providing a platform for the much-heralded long-distance spin communication ~ 8 – 20 micrometer between solid-state spin qubits. Finally, I should touch upon the recent experimental realization of the intrinsic spin Hall effect in two-subband quantum wells, its theoretical explanation, and extensions in the context of wurtzite systems.