This book explores interesting possibilities of extracting information about quantum states from data readily obtained from experiments, such as tomograms and expectation values of appropriate observables. The procedures suggested for identifying nonclassical effects such as wave packet revivals, squeezing and entanglement solely from tomograms circumvent detailed state reconstruction. Several bipartite entanglement indicators are defined based on tomograms, and their efficacy assessed in models of atom-field interactions and qubit systems. Tools of classical ergodic theory such as time series and network analysis are applied to quantum observables treated as dynamical variables. This brings out novel aspects involving different time scales. The book is aimed at researchers in the areas of quantum optics and quantum dynamics.