Black-Scholes assumes constant volatility, but real markets show systematic patterns in implied vol across strike and expiry. Plot IV against strike at one expiry: in equity index options, the curve is downward-sloping (lower-strike puts have higher IV than higher-strike calls) — a "skew." In FX options, the curve is more symmetric, called a "smile."
Across expiries, IV typically rises with maturity (a "term structure") because uncertainty grows over time. The full two-dimensional surface IV(strike, maturity) is the volatility surface — a fundamental object for any options book.
Causes: skew reflects fat-tailed return distributions, demand for crash protection (puts), and risk-aversion. Smile reflects realized jumps. The surface moves over time and is itself a tradable object via vol-of-vol products.
Practical use: market makers quote and hedge in vol space. Pricing exotics requires interpolating the surface and being careful about no-arbitrage constraints (calendar arbitrage, butterfly arbitrage).