Cardiovascular disorders account for nearly 1 in 3 deaths in the United States. Care for these disorders are often determined during visits to acute care facilities, such as hospitals. While the length of stay in these settings represents just a small proportion of patients' lives, they account for a disproportionately large amount of decision making. To overcome this bias towards data from acute care settings, there is a need for longitudinal monitoring in patients with cardiovascular disorders. Longitudinal monitoring can provide a more comprehensive picture of patient health, allowing for more informed decision making. This work surveys the current field of sensing technologies and machine learning analytics that exist in the field of remote monitoring for cardiovascular disorders. We highlight three primary needs in the design of new smart health technologies: 1) the need for sensing technology that can track longitudinal trends in signs and symptoms of the cardiovascular disorder despite potentially infrequent, noisy, or missing data measurements; 2) the need for new analytic techniques that model data captured in a longitudinal, continual fashion to aid in the development of new risk prediction techniques and in tracking disease progression; and 3) the need for machine learning techniques that are personalized and interpretable, allowing for advancements in shared clinical decision making. We highlight these needs based upon the current state-of-the-art in smart health technologies and analytics and discuss the ample opportunities that exist in addressing all three needs in the development of smart health technologies and analytics applied to the field of cardiovascular disorders and care.