Crime and underground economic activity are a fact of life around the world. Most societies attempt to control these activities through the expenditure of resources on monitoring, prosecution, punishment, and educational programmes. Gathering statistics about who is engaging in illegal or underground activity, the frequencies with which various crimes or underground transactions are occurring, and the severity or magnitude of these acts, is crucial for making good decisions regarding our allocation of resources in this area. Unfortunately, in general it is very difficult to obtain accurate information about these issues. This is partly because the individuals engaged in such activities wish not to be identified and often take actions to avoid detection, and partly because by their very nature the activities tend not to generate economic, accounting, legal, demographic or other cultural records. The fact that it is difficult to obtain accurate information about the activities, however, does not in any way imply that we should not make a concerted effort to try to obtain the best information we can. I believe the cost associated with attempting to determine the extent and nature of these activities is in most circumstances well below the expected benefit, which includes the likelihood of improved decisionmaking by relevant government personnel and the general public. As a result, I also believe the debate about developing estimates of illegal or underground economic activity should primarily focus on practical issues related to how best to go about developing estimates that are as reliable as possible. In this short article I shall discuss the measurement of noncompliance with laws and regulations, my particular area of expertise, and shall not discuss the measurement of other kinds of 'hidden' economic behaviours, such as informal contracting, unmeasured home production, and 'grey-market' activities. In particular, I shall discuss three approaches for estimating the aggregate amount of noncompliance with respect to a specific law or regulation, (i) intensive data collection for a focused subsample of the population, (ii) detection controlled estimation, and (iii) the comparision of estimates generated by distinct datasets and models. For each, I shall describe in general terms what the approach is and how it is implemented, review limitations of the approach, and present an example of the application of the approach to the measurement of tax noncompliance in the United States. My discussion shall necessarily be short and I refer the interested reader to a variety of original research publications for more details, especially about the specific examples.