Rinse the capers and, if you are using capers in salt, soak them in cold water for 5 minutes, then drain; if using capers in brine, simply rinse, then drain.
Meanwhile, heat the oil in a large frying pan over a low heat. Add the chillies, garlic and anchovies and cook, stirring, for 2 minutes until the anchovies begin to melt into the oil. Increase the heat to high, add the capers and cook, stirring, for 1 minute. Add the tomatoes and olives, season with salt and bring to the boil. Leave the sauce to boil rapidly while you cook the pasta.
Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente. Drain, reserving a ladleful of the cooking water. Stir the pasta into the sauce, tossing until well combined. Add the reserved pasta cooking water and continue stirring until the pasta is well coated and looks silky. Serve immediately.