After a brief overview of previous work on probabilistic transient stability assessment, it is shown how to obtain the probability of transient instability and how the different types of uncertainty can be included. An evaluation is made of the severity or consequences of the loss of a generator caused by an out of step condition. While calculating the probability, the transient stability performance of the system needs to be quantified for several fault location and fault types. For this purpose the Transient Stability Index (TSI) is used. This index is based on the transient energy components calculated at each step of a time domain simulation. It allows a fast and accurate measurement of the degree of stability of the system facing a fault. One way to present the results is to plot the risk as a function of a single operating parameter. Another type of graphs is the risk equivalent of the traditional it nomograms: instead of presenting the N- 1 security boundaries, it shows contours of equal risk. Both type of plots must be updated when operating conditions change. A large number of risk values are required in real time to update the plots. As a result of the numerous time domain simulations, the calculation process becomes very heavy. To speed up the process, a neural network has been trained to predict the stability index of the system given a fault of a certain type at a certain location under the current operating conditions. This neural network is used to replace the slower time-domain simulation. To illustrate the usefulness of risk-based transient assessment, a few applications are presented. Several risk plots will be displayed and discussed as well as equal-risk contour plots obtained with neural networks. Finally, it is explained how the use of risk can be included in operational decision-making problems.