Soil shrinkage is the change in soil bulk specific volume with water content. It is usually considered to occur in the case of swelling soils, but indeed occurs and can be measured on most so-called rigid soils. The first attempts to quantify soil structure with shrinkage measurement and modelling are 100 years old, and repeated efforts where made along the 20th century, on both experimental and theoretical sides. Considerable technical improvements allowed to continuously measure shrinkage curves on undisturbed soil samples or in situ, and supported the development of a new knowledge and new models of soil shrinkage. The methods can be split in two categories: continuous and discrete measurement, the latter dealing most often with a series of samples for a single shrinkage curve measurement. The continuous measurement methods are based on either 3 dimensional or 1 dimensional (1-D) measurements, accompanied or not by water retention curve (WRC) measurement. The advantages and limitations of the several methods are discussed. The use of continuous 1-D measurement with simultaneous WRC is proposed as a cheap, easy to handle, reliable method. Recently proposed models are classified and reviewed. The conceptual models are described and compared, and their application to soil structure quantification is discussed on the basis of experimental results. The application of shrinkage modelling to structure characterization on a wide range of soil type and clay content is presented, and the present issues and perspectives of the research field are summarized.