This paper intends to consolidate the theory of risk management into practical applications in geotechnical engineering, presenting concepts, clarifying procedures and discussing openly its difficulties and trends. It brings the evolution of the risk concept and its application to engineering, worldwide and in Brazil, showing the trend of risk management as a decision-making tool in engineering with fair acceptance by the society. The probabilistic approach is discussed and compared to the deterministic one, focusing on the obtaining of reliability indexes and failure probabilities for engineering structures. For this, quantitative methods, such as event and fault tree analyses and probabilistic methods, are reviewed, discussing their applications and comparinPg their advantages and disadvantages. Risk metrics and the evaluation of its two components, failure probability and consequences due to failure, are presented, focusing on the need to quantify and monetise consequences, and, consequently, the engineering risks. From this derives the concept of overall cost, which is the structure cost or value added to its risk value, providing an efficient tool to compare engineering alternatives and solutions. Finally, the risk management scheme is discussed, focusing on the need to establish an intelligent risk management system, which incorporates an automatic and intelligent communication tool, to disseminate among professionals, company hierarchy and outside stakeholders, the structure risks, according to their levels in the Risk Diagram and guided by the company Risk Policy. This is illustrated by examples of applications in two geotechnical structures (a dam and an urban tunnel), showing its enormous potential as a decision-making tool in engineering, using risk-based or risk-informed approach.