Many screening trials conducted in the past have generated a wealth of interesting data. These data represent an invaluable source of information for furthering our knowledge about the natural history of the disease. The traditional approach to modeling cancer screening tends to describe the process of tumor development in only one dimension, that is, the time natural history. A broader methodological idea is to construct a stochastic model of cancer development and detection that yields the multivariate distribution of observable variables at the time of diagnosis. By focusing on such multivariate observations, rather than just on the age of patients at diagnosis, this idea seeks to invoke an additional source of information (available only at the time of detection) in order to improve an estimation of unobservable quantitative parameters of cancer latency. In this article, we discuss modeling techniques that make the above-mentioned problems approachable. A special focus is placed on analytical tools for deriving joint distributions of clinical covariates at the time of cancer detection under an arbitrary screening protocol. In addition, some future research avenues and public health implications of the proposed approach are discussed.