The main challenge of modern computational materials physics consists in 
both the understanding and the predictive modelling of phenomena at 
the very atomic scale, i.e. in the realm of the quantum mechanical 
description of chemical bonding.  Unfortunately, while a self-consistent
quantum simulation has in principle the proper accuracy to face with such a 
challenge, its computational workload is often overwhelming. This 
"accuracy vs. workload" dilemma has forced the scientific community to 
develop different solutions for spanning length and time scales as large 
as needed. In this seminar I will present the semi-empirical tight-binding 
molecular dynamics scheme - representing a conceptual bridge between quantum 
and empirical simulations - by focussing on its  low-complexity  
(linear-scaling) implementation and on the temperature-accelerated
dynamics scheme. Both developments allow for quantum simulations with 
unprecedented system size and time extension, as extensively discussed 
by means of solid-state physics applications.