In this thesis we theoretically investigate effects of the interaction between electron spins and nuclear spins in different nanoscopic devices, quantum dots and spin valves. A quantum dot is a tiny potential well in which one can trap single electrons. One of the proposed applications of the quantum dot is to use the spin of the trapped electrons as qubits, the computational units in a quantum computer. The main obstacle for this application is the fact that the electron spin in the dot is coupled via the hyperfine interaction to roughly one million randomly fluctuating nuclear spins (those in the host material of the quantum dot). These fluctuations manifest themselves as a small but unpredictable magnetic field, causing the spin state of the electron to be not stable enough to be useful for quantum computation. The hyperfine interaction however works both ways: Several recent experiments have showed clear evidence that the nuclear spins, in turn, are also affected by the electron spin. So, it might be possible to suppress the fluctuations of the nuclear field by a clever manipulation of the electron spin in the dot. If so, this would bring the realization of the quantum dot spin qubit one big step closer. In this thesis we investigate the coupled electron-nuclear spin dynamics in several realistic experimental situations. We consider both single and double quantum dots, and concentrate on the combination of electronic transport (current) and electron spin resonance (a magnetic microwave field). We find that in these situations the fluctuations of the nuclear field indeed can be strongly suppressed, and we support this with experimental results. Further, we investigate the effect of strong spin-orbit coupling on the transport properties of a double quantum dot, and we also consider hyperfine effects in a metallic spin valve.