  Natural systems are typically nonlinear and complex, and it is of great
interest to be able to reconstruct a system in order to understand its
mechanism, which can not only recover nonlinear behaviors but also predict
future dynamics. Due to the advances of modern technology, big data becomes
increasingly accessible and consequently the problem of reconstructing systems
from measured data or time series plays a central role in many scientific
disciplines. In recent decades, nonlinear methods rooted in state space
reconstruction have been developed, and they do not assume any model equations
but can recover the dynamics purely from the measured time series data. In this
review, the development of state space reconstruction techniques will be
introduced and the recent advances in systems prediction and causality
inference using state space reconstruction will be presented. Particularly, the
cutting-edge method to deal with short-term time series data will be focused.
Finally, the advantages as well as the remaining problems in this field are
discussed.
