The risk of airborne viral contagion in indoor spaces is a multidisciplinary problem involving a wide range of parameters. From a fluid mechanics perspective, the problem of infectivity can be divided into an ejection-scale problem and a room-scale problem. The ejection-scale problem aims to answer the question of what range of droplet sizes remain airborne as a result of expiration activities of a sick person. A theoretical framework was developed to answer this question and validated with high-fidelity simulations. It is shown that the risk of infection is heightened when the droplet evaporation rate is fast, i.e., under hot and dry ambient conditions. The room-scale problem is then considered to examine the probability of contagion on a longer time scale. Well-mixed models have been used extensively to solve the problem of infectivity at the room-scale. However, it is reasonable to expect that a perfectly well-mixed state cannot be achieved at any realistic level of ventilation. We test the robustness of the well-mixed theory at four levels. Results show that the well-mixed theory is accurate in predicting the viral concentration only when averaged over the entire room. The prediction could be substantially off at separation distances under 2m and over 6 m. A simple correction function is introduced to account for departure from the well-mixed theory. Based on this accurate and rapid predictions can be made that are applicable for a wide range of ventilation conditions (ACH, filtration, etc), wide range of ejection activities (breathing, speaking, singing), for any source-sink separation distance. This framework can also be used to answer questions such as if higher air-change-per-hour (ACH) always better?