Within the field tissue engineering, new and novel approaches to bone and cartilage regeneration have been explored. These novel approaches are being developed in order to mediate and expedite the natural healing process. Electrospinning is a well-established nano-/microtechnique for the manufacture of biomimetic fibrous constructs for various tissue growth and healing. This review will focus on recent advancements in the area of tissue-engineered construct fabrication via electrospinning-based technologies with emphasis on multimaterial electrospinning, incorporation of morphogenetic/bioactive factors, as well as the combination of electrospraying for bone and cartilage regeneration. The review will also place special emphasis on novel biologically inspired nanomaterials for electrospun nanocomposites.