Let X be our favorite space of continuous functions on $R^n$, and let f be a real-valued function defined on some awful subset E of $R^n$. How can we decide whether f extends to a function F in X? If F exists, then how small can we take its norm? What can we say about the derivatives of F (if they exist)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F with close to least-possible norm? How many computer operations does it take? What if F is required merely to agree approximately with f on E? Which points of E should we delete as "outliers"? The subject goes back to Whitney. The recent results are joint work with Arie Israel, Bo'az Klartag and Garving Luli.