Safely developing self-driving vehicles presents technical challenges. Among the key technical challenges are how to confidently demonstrate the safety of a self-driving vehicle when the number of permutations of operating conditions, scenarios, system inputs, etc. are complex, uncertain, and potentially limitless. This paper provides a broad survey of the various types of uncertainty in the development of self-driving vehicles and will outline several possible strategies for handling uncertainty. Advantages and challenges of different approaches, including qualitative and quantitative methods, will also be discussed.