The goal of tissue engineering is to mitigate the critical shortage of donor organs via in vitro fabrication of functional biological structures. Tissue engineering is one of the most prominent examples of interdisciplinary fields, where scientists with different backgrounds work together to boost the quality of life by addressing critical health issues. Many different fields, such as developmental and molecular biology, as well as technologies, such as micro- and nanotechnologies and additive manufacturing, have been integral for advancing the field of tissue engineering. Over the past 20 years, spectacular advancements have been achieved to harness nature's ability to cure diseased tissues and organs. Patients have received laboratory-grown tissues and organs made out of their own cells, thus eliminating the risk of rejection. However, challenges remain when addressing more complex solid organs such as the heart, liver, and kidney. Herein, we review recent accomplishments as well as challenges that must be addressed in the field of tissue engineering and provide a perspective regarding strategies in further development.