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.