Injuries of the bone/cartilage and central nervous system are still a serious socio-economic problem. They are an effect of diversified, difficult-to-access tissue structures as well as complex regeneration mechanisms. Currently, commercially available materials partially solve this problem, but they do not fulfill all of the bone/cartilage and neural tissue engineering requirements such as mechanical properties, biochemical cues or adequate biodegradation. There are still many things to do to provide complete restoration of injured tissues. Recent reports in bone/cartilage and neural tissue engineering give high hopes in designing scaffolds for complete tissue regeneration. This review thoroughly discusses the advantages and disadvantages of currently available commercial scaffolds and sheds new light on the designing of novel polymeric scaffolds composed of hydrogels, electrospun nanofibers, or hydrogels loaded with nano-additives.