The World Health Organization (WHO) has declared COVID-19 a pandemic. We review and reduce the clinical literature on diagnosis of COVID-19 through symptoms that might be remotely detected as of early May 2020. Vital signs associated with respiratory distress and fever, coughing, and visible infections have been reported. Fever screening by temperature monitoring is currently popular. However, improved noncontact detection is sought. Vital signs including heart rate and respiratory rate are affected by the condition. Cough, fatigue, and visible infections are also reported as common symptoms. There are non-contact methods for measuring vital signs remotely that have been shown to have acceptable accuracy, reliability, and practicality in some settings. Each has its pros and cons and may perform well in some challenges but be inadequate in others. Our review shows that visible spectrum and thermal spectrum cameras offer the best options for truly noncontact sensing of those studied to date, thermal cameras due to their potential to measure all likely symptoms on a single camera, especially temperature, and video cameras due to their availability, cost, adaptability, and compatibility. Substantial supply chain disruptions during the pandemic and the widespread nature of the problem means that cost-effectiveness and availability are important considerations.