Female breast cancer was the most prevalent cancer worldwide in 2020, according to the Global Cancer Observatory. As a prophylactic measure or as a treatment, mastectomy and lumpectomy are often performed at women. Following these surgeries, women normally do a breast reconstruction to minimize the impact on their physical appearance and, hence, on their mental health, associated with self-image issues. Nowadays, breast reconstruction is based on autologous tissues or implants, which both have disadvantages, such as volume loss over time or capsular contracture, respectively. Tissue engineering and regenerative medicine can bring better solutions and overcome these current limitations. Even though more knowledge needs to be acquired, the combination of biomaterial scaffolds and autologous cells appears to be a promising approach for breast reconstruction. With the growth and improvement of additive manufacturing, three dimensional (3D) printing has been demonstrating a lot of potential to produce complex scaffolds with high resolution. Natural and synthetic materials have been studied in this context and seeded mainly with adipose derived stem cells (ADSCs) since they have a high capability of differentiation. The scaffold must mimic the environment of the extracellular matrix (ECM) of the native tissue, being a structural support for cells to adhere, proliferate and migrate. Hydrogels (e.g., gelatin, alginate, collagen, and fibrin) have been a biomaterial widely studied for this purpose since their matrix resembles the natural ECM of the native tissues. A powerful tool that can be used in parallel with experimental techniques is finite element (FE) modeling, which can aid the measurement of mechanical properties of either breast tissues or scaffolds. FE models may help in the simulation of the whole breast or scaffold under different conditions, predicting what might happen in real life. Therefore, this review gives an overall summary concerning the human breast, specifically its mechanical properties using experimental and FE analysis, and the tissue engineering approaches to regenerate this particular tissue, along with FE models.