This book explores interesting possibilities of extracting information about quantum statesfrom data readily obtained from experiments, such as tomograms and expectation values ofappropriate observables. The procedures suggested for identifying nonclassical effects suchas wave packet revivals, squeezing and entanglement solely from tomograms circumventdetailed state reconstruction. Several bipartite entanglement indicators are defined basedon tomograms, and their efficacy assessed in models of atom-field interactions and qubitsystems. Tools of classical ergodic theory such as time series and network analysis areapplied to quantum observables treated as dynamical variables. This brings out novelaspects involving different time scales. The book is aimed at researchers in the areas ofquantum optics and quantum dynamics.