In 2006, Košmrlj obtained Diploma (B. Sc.) in Mathematical Physics from the University of Ljubljana, Slovenia. He then moved to Massachusetts Institute of Technology for his graduate studies in physics, where he was coadvised by Arup Chakraborty and Mehran Kardar. For PhD thesis Košmrlj studied the development of immune system and its response to infecting microorganisms. After receiving PhD in 2011, Košmrlj became postdoc with David Nelson at Harvard University, where he worked on mechanics of thin membranes and metamaterials.

In 2015 Košmrlj became assistant professor at Princeton University, where he continues theoretical and computational research of complex systems ranging from materials science to the physics of living systems. Current research includes the design and mechanics of metamaterials, where geometrical shape of structures gives rise to unusual material properties. This includes the role of geometry and topology on the mechanics of structures both at the macro-scale and at the micro-scale, where effects of thermal fluctuations and disorder could be important if one wants to design flexible electronics, sensitive force sensors or micro-actuators. Current research also investigates the role of mechanics in biological systems, such as mechanics in morphogenesis during embryo development.