Tissue engineering is a very promising field of regenerative medicine. Life expectancy has been increasing, and tissue replacement is increasingly needed in patients suffering from various degenerative disorders of the organs. The use of adult mesenchymal stem cells (e.g. from adipose tissue or from bone marrow) in tissue engineering seems to be a promising approach for tissue replacements. Clinical applications can make direct use of the large secretome of these cells, which can have a positive influence on other cells around. Another advantage of adult mesenchymal stem cells is the possibility to differentiate them into various mature cells via appropriate culture conditions (i.e. medium composition, biomaterial properties, and dynamic conditions). This review is focused on current and future ways to carry out tissue replacement of damaged bones and blood vessels, especially with the use of suitable adult mesenchymal stem cells as a potential source of differentiated mature cells that can later be used for tissue replacement. The advantages and disadvantages of different stem cell sources are discussed, with a main focus on adipose-derived stem cells. Patient factors that can influence later clinical applications are taken into account.