The development of three-dimensional (3D) scaffolds with physical and chemical topological cues at the macro-, micro-, and nanometer scale is urgently needed for successful tissue engineering applications. 3D scaffolds can be manufactured by a wide variety of techniques. Electrospinning technology has emerged as a powerful manufacturing technique to produce non-woven nanofibrous scaffolds with very interesting features for tissue engineering products. However, electrospun scaffolds have some inherent limitations that compromise the regeneration of thick and complex tissues. By integrating electrospinning and other fabrication technologies, multifunctional 3D fibrous assemblies with micro/nanotopographical features can be created. The proper combination of techniques leads to materials with nano and macro-structure, allowing an improvement in the biological performance of tissue-engineered constructs. In this review, we focus on the most relevant strategies to produce electrospun polymer/composite scaffolds with 3D architecture. A detailed description of procedures involving physical and chemical agents to create structures with large pores and 3D fiber assemblies is introduced. Finally, characterization and biological assays including in vitro and in vivo studies of structures intended for the regeneration of functional tissues are briefly presented and discussed.