Increasing development of the urban environment and supporting infrastructure systems has necessitated a greater use of underground space and sites that were hitherto judged to be non economically viable (e.g. because of difficult ground conditions, high groundwater levels, steeply sloping ground). This presents many challenges in terms of planning, design and construction as well as the protection of existing buildings. Understanding the complex nature of soil – structure interaction and the resulting ground movements is of fundamental importance to assess developments involving the new construction of tunnels and underground spaces. There is strong concern that any potential damage resulting from such works must be minimized, particularly for historic and sensitive structures. Damage can affect both the existing and new structures. Quantifying degrees of damage and assessing whether they are of aesthetic or structural significance are important. Minimizing damage is clearly desirable: both to protect the interest of the public and building owners and to avoid protracted claims and eventual losses. Consequently the ability to predict with confidence tunnelling induced settlements and the associate potential for damage to structures is of paramount importance. The aim of the article is to outline, with reference to the most recent literature, the state of the art of the methods for estimating ground movements caused by tunnelling. The construction of tunnels inevitably results in movement of the ground around them. At the ground surface these movements manifest themselves in what is termed a “settlement trough”. For “greenfield sites”, the shape of this trough transverse to the axis of tunnel approximates closely to a Gaussian normal distribution curve. Many authors have summarized the current widely used empirical approach to the prediction of immediate surface and near-surface ground displacements. These empirical equations provide a simple means for estimating the near – surface displacements caused by tunnelling, assuming “greenfield” conditions, that is ignoring the presence of any building or structure. However, in the paper, it is shown that the approach based on these empirical equations can be adopted only for a preliminary assessment because, even for greeenfield conditions, the obtained prediction of ground movements caused by tunnelling is not realistic. An example, about the excavation of an highway tunnel, shows that to develop a rational and realistic approach to the evaluation of the tunnelling – induced ground movements and to the assessment of risk of damage to buildings owing to tunnelling, it is absolutely necessary to carry out numerical analyses. The numerical analyses are in fact the only ones that allow to take into account, properly and realistically, the type of ground, the groundwater conditions, the tunnelling method, the length of time in providing positive support and the quality of supervision and control. In conclusion a rational and coherent approach to predicting potential building damage is described where the axial and bending stiffness of the building can be taken into account. This method is based on the results from an extensive series of numerical parametric studies that were carried out varying building stiffness and geometry and it is a staged process with a preliminary assessment, second stage assessment and detailed evaluation (COST; European initiative Co-operation in Science and Technology).