Constitutive models are an essential part of computational modelling in geotechnics; they are at the heart of almost all theoretical predictions of geotechnical structures. How the stress-strain (and perhaps time) response of soil (and rock) is represented in these mathematical models is usually the key to successful prediction of the behavior of geotechnical structures. However, the important details of these models, particularly the idealisations that are made, may be poorly or incompletely understood, or ignored, sometimes at significant cost to the unwary analyst. Indeed, the capabilities and the shortcomings of these models, especially the more advanced models, are not always easy to ascertain. In some cases, determination of the values of the input parameters is not straightforward. Consequently, it may be difficult to determine which model to select for a particular task. This lecture will explore some of the more important developments in the constitutive modelling of soils and will attempt to address some of these issues of potential concern. The need for such models and the various attributes and capabilities that the commonly used models possess will be reviewed. Also discussed is the issue of matching a particular model to the geotechnical problem at hand, which model attributes are required and why. The intention is to place emphasis in this lecture on the physical basis of these models, rather than explore their mathematical complexity in detail. Some of the constitutive models encoded in the software packages used routinely in geotechnical practice are reviewed, and discussion is also provided on their specific limitations. Examples of practical applications, involving the solution of boundary and initial value problems, are described to illustrate both the advantages and some of the limitations of both commonly used and highly advanced constitutive models.