Emerging research highlights the complex inter-relationships between sleep disordered breathing and cardiovascular disease, presenting clinical and research opportunities as well as challenges. Patients presenting to cardiology clinics have a high prevalence of obstructive (OSA) and central sleep apnea associated with Cheyne-Stokes Respiration (CSA-CSR). Multiple mechanisms have been identified by which sleep disturbances adversely affect cardiovascular structure and function. Epidemiological research indicates that OSA is associated with increases in the incidence and progression of coronary heart disease, heart failure, stroke and atrial fibrillation. CSA-CSR predicts incident heart failure and atrial fibrillation; among patients with heart failure, CSA-CSR strongly predicts mortality. Thus, a strong literature provides the mechanistic and empirical bases for considering OSA and CSA-CSR as potentially modifiable risk factors for cardiovascular disease. Data from small trials provide evidence that treatment of OSA with continuous positive airway pressure (CPAP) not only improves patient-reported outcomes such as sleepiness, quality of life and mood, but also improves intermediate cardiovascular endpoints such as blood pressure, cardiac ejection fraction, vascular parameters and arrhythmias. However, data from large scale randomized controlled trials do not currently support a role for positive pressure therapies for reducing cardiovascular mortality. The results of two recent large randomized controlled trials, published in 2015 and 2016, raise questions on the effectiveness of pressure therapies in reducing clinical endpoints, although one supported the beneficial effect of CPAP on quality of life, mood, and work absenteeism. This review provides a contextual framework for interpreting the results of recent studies, key clinical messages, and suggestions for future sleep and cardiovascular research, which include further consideration of individual risk factors, use of existing and new multi-modality therapies which also address adherence, and implementation of trials that are sufficiently powered to target endpoints and to support subgroup analyses. These goals may best be addressed through strengthening collaboration among cardiology, sleep medicine and clinical trial communities.