Hidden Markov models (HMMs) are useful for applications in many areas, including engineering and the biological sciences. In this article, we show how adaptations of the standard HMM can be developed for the analysis of important applications in Cancer Epidemiology and Genetics. We show how HMMs can be used to integrate antigraphy data from intensively collected longitudinal data from wearable devices and self-reported sleep data to estimate the sleep-wake cycle. Next, we show the application of HMMs for studying the progression of healthy women to the diagnosis of cervical cancer. We then show the application of HMMs to changepoint detection in cancer surveillance. Last, we show how HMMs can provide insight into the biological mechanisms in somatic (tumor) copy number mutations in cancer patients. All these applications involve novel adaptations of the forward-backward algorithm that is commonly used to compute the E-step in the E-M algorithm, which has been commonly applied for maximum likelihood in this setting.