How classical chaos emerges from the underlying quantum world is a fundamental problem in Physics. The origin of this question is in the correspondence principle, which states that quantum mechanics, the physical theory of microscopic objects, should reproduce classical laws in the macroscopic limit. Studying a quantum system whose classical analog is chaotic, we can understand the quantum features that lead to classical chaos in the classical limit. We use kicked tops of a few qubits in the deep quantum regime to investigate the onset of chaos. We analyze a couple of the dynamical diagnostics of chaos called OTOCs and Loschmidt echo in this study. We find residual signatures of classical chaos even in the deep quantum regime. Another domain where one can study the effects of chaos is quantum state tomography. Quantum state reconstruction is a nontrivial problem in itself because of the inherent quantum uncertainty. Traditional projective measurements to find out information about the state require an infinite number of copies of the system. A continuous weak measurement protocol performed on a finite ensemble of the system can get around this. We find that good fidelity reconstruction of random states does not require an informationally complete set of measurements. The effect of chaotic dynamics in tomography is investigated. We also provide an exponentially efficient protocol to measure OTOCs, a quantifier of chaos, using a single pure qubit quantum computation (DQC1) protocol. This protocol also helps to benchmark unitary gates, which is important from the perspective of quantum computation and quantum control.