Variance swaps have become, for many portfolio managers, the leading tool for managing exposure to volatility risk. Variance swaps pay the realized variance of the underlying, where realized variance is typically defined to be the sum of squared daily returns. Moreover, a second generation of variance derivatives has emerged, including variance _options_ (calls and puts on realized variance) which offer portfolio managers even greater control over their volatility risk profile. However, they present greater pricing/hedging problems to the dealer. We take a robust model-free approach to these problems. Assuming essentially only the positivity and continuity of the underlying share price, we hedge variance options by dynamically trading the underlying shares, and statically holding European options. These hedges lead to upper and lower bounds on variance option values. This work is joint with Peter Carr.