Our understanding of communicable disease prevention and control is rooted in the theory of host population transmission dynamics. To this end, the network of host-to-host contacts along which the transmission can occur drives the disease spreading. Network theory provides, thus, tools for assessing the potential for sustained spreading, and understanding the pattern and the velocity of the latter. Recently different types of sensors and devices allow mining highly resolved host contact data in space and time in different contexts relevant for disease spread. Data availability reveals the temporal dimension of such systems and pushes the development of new approaches for the identification of the temporal aspects of the contact patterns that are critical for disease transmission. The talk will focus on risk assessment analyses based on the identification of the epidemic threshold, the critical infection transmissibility value separating disease extinction from sustained spreading. I will present a theoretical framework, the infection propagator approach, able to assess this quantity for the case of host-to-host contact networks that are variable in time [1,2]. The approach relays on the knowledge of the sequence of adjacency matrices describing the temporal network and is rooted in a multi-layer representation of the latter that preserves the network causality. It employs a tensor formulation that integrates both spreading and network dynamics and allows for the analytical solution of the linearized Markov chain description of the spreading process, extending in this way the quenched approach to the time-varying case. I will discuss the mathematical formulation of the approach for various disease compartmental schemes, SIS, SIR, SIRS [1,2] and SEIS models and I will present examples of how this can be applied to epidemiological situations of interest to provide insights on the factors driving the epidemic risk. [1] Analytical computation of the epidemic threshold on temporal networks E. Valdano, L. Ferreri, C. Poletto, V. Colizza, Physics Review X 5 021005 (2015) [2] Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution, E. Valdano, C. Poletto, V. Colizza, the European Physical Journal B, 88: 341 (2015)