The construction of synthetic cells is a rapidly growing discipline. In this review, we discuss the last advances of the bottom-up constructive approach, in particular the construction of minimal cells. Three different paths are used to assemble cells from molecular components. The construction of protocells explores questions related to the origin of life using prebiotic molecules. The construction of minimal cells from natural molecules consists of integrating the DNA information and a simple metabolism into vesicles with the rather ambitious objective of obtaining a compartment capable of self-reproduction based on a minimal genome. The artificial cell approach consists of assembling cell-sized compartments capable of biological functions by integrating natural and synthetic molecules to construct hybrid systems with new properties. Those three avenues, all multidisciplinary and complementary, give rise to new ideas for biotechnologies and medicine.