In this review, materials based on polymers and hybrids possessing both organic and inorganic contents for repairing or facilitating cell growth in tissue engineering are discussed. Pure polymer based biomaterials are predominantly used to target soft tissues. Stipulated by possibilities of tuning the composition and concentration of their inorganic content, hybrid materials allow to mimic properties of various types of harder tissues. That leads to the concept of “one-matches-all” referring to materials possessing the same polymeric base, but different inorganic content to enable tissue growth and repair, proliferation of cells, and the formation of the ECM (extra cellular matrix). Furthermore, adding drug delivery carriers to coatings and scaffolds designed with such materials brings additional functionality by encapsulating active molecules, antibacterial agents, and growth factors. We discuss here materials and methods of their assembly from a general perspective together with their applications in various tissue engineering sub-areas: interstitial, connective, vascular, nervous, visceral and musculoskeletal tissues. The overall aims of this review are two-fold: (a) to describe the needs and opportunities in the field of bio-medicine, which should be useful for material scientists, and (b) to present capabilities and resources available in the area of materials, which should be of interest for biologists and medical doctors.