  In this article, we review the interdisciplinary techniques (borrowed from
physics, mathematics, statistics, machine-learning, etc.) and methodological
framework that we have used to understand climate systems, which serve as
examples of "complex systems". We believe that this would offer valuable
insights to comprehend the complexity of climate variability and pave the way
for drafting policies for action against climate change, etc. Our basic aim is
to analyse time-series data structures across diverse climate parameters,
extract Fourier-transformed features to recognize and model the
trends/seasonalities in the climate variables using standard methods like
detrended residual series analyses, correlation structures among climate
parameters, Granger causal models, and other statistical machine-learning
techniques. We cite and briefly explain two case studies: (i) the relationship
between the Standardised Precipitation Index (SPI) and specific climate
variables including Sea Surface Temperature (SST), El Ni\~no Southern
Oscillation (ENSO), and Indian Ocean Dipole (IOD), uncovering temporal shifts
in correlations between SPI and these variables, and reveal complex patterns
that drive drought and wet climate conditions in South-West Australia; (ii) the
complex interactions of North Atlantic Oscillation (NAO) index, with SST and
sea ice extent (SIE), potentially arising from positive feedback loops.
