The exact simulation of quantum mechanical systems on classical computers generally scales exponentially with the size of the system N. Using quantum computers, the computational resources required to carry out the simulation are polynomial. Our group has been working in the development and characterization of quantum computational algorithms for the simulation of chemical systems. We will give a tutorial on our algorithms for the simulation of molecular electronic structure, molecular properties and quantum dynamics, and will discuss the opportunities, open questions and challenges in the field of simulation of physical systems using quantum computers or dedicated quantum devices.