1. Introduction
2. Synoptic Surveys
3. Core-Collapse Supernovae in a Cosmic Context
3.1. The Cosmic Core-Collapse Supernova Rate: Expectations
3.2. The Effect of Dust Obscuration
3.3. Supernova Observability at Cosmic Distances
3.4. Supernova Discovery in Magnitude-Limited Surveys
4. The Cosmic Core-Collapse Supernova Rate: Forecasts for Synoptic Surveys
4.1. Connecting Cosmic Supernovae and Survey Observables
4.2. Forecasts for Synoptic Surveys
5. Dust Obscuration: Disentangling the Degeneracies and Probing High-Redshift Star-Forming Environments
6. Discussion
6.1. Survey Impact on the Cosmic Supernova and Star Formation Histories
6.2. Survey Supernovae as Distance Indicators: the Expanding Photosphere Method
6.3. Other Science with Cosmic Supernovae
6.4. Comparison with Type Ia Survey Requirements
6.5. Redshifts and Typing from Photometry and Followup Spectroscopy