The Black-Scholes model is one of the most influential equations in finance. It is also structurally wrong in ways every practitioner works around daily. Understanding where it breaks is more useful than understanding the formula itself.
Constant volatility
The model assumes $\sigma$ is a fixed number over the life of the option. In reality, volatility clusters (high vol follows high vol), jumps (a news event can move realized vol from 20% to 80% in a day), and exhibits mean reversion. The entire volatility smile exists because the market knows this and prices options accordingly.
On Deribit, I see this directly. ATM IV on BTC might be 52%, but puts 7% out of the money show IVs above 100% at 0-DTE. The model says all strikes should have the same IV. The market disagrees violently.
Log-normal returns
The model assumes returns follow $dS = \mu S \, dt + \sigma S \, dW$, which implies log-normal prices. This makes large moves extremely rare. In practice, markets produce fat tails. BTC in particular has historically delivered moves of 5+ standard deviations far more often than the model predicts. This is why OTM options trade at elevated IVs: the market charges for events the model says should almost never happen.
Continuous hedging
The Black-Scholes derivation depends on continuously rebalancing a delta hedge. In reality, you cannot trade continuously. Markets close (traditional) or liquidity dries up (crypto at 3am). Prices gap. Each gap breaks the hedge and introduces realized P&L that deviates from the model. This is the gap risk that makes short gamma positions dangerous overnight.
What practitioners use
Nobody prices options with raw Black-Scholes anymore. The model serves as a quoting convention: traders quote in IV, which is the Black-Scholes input that reproduces the market price. Actual pricing uses stochastic volatility models (Heston), jump-diffusion (Merton), or calibrated local volatility surfaces.
For my work on Deribit, the practical approach is Black-76 (the futures-settled variant) as the computational engine, with smile adjustments layered on top. The model provides the Greeks and the language. The adjustments provide the accuracy. Neither works without the other.