  In the face of the upcoming 30th anniversary of econophysics, we review our
contributions and other related works on the modeling of the long-range memory
phenomenon in physical, economic, and other social complex systems. Our group
has shown that the long-range memory phenomenon can be reproduced using various
Markov processes, such as point processes, stochastic differential equations
and agent-based models. Reproduced well enough to match other statistical
properties of the financial markets, such as return and trading activity
distributions and first-passage time distributions. Research has lead us to
question whether the observed long-range memory is a result of actual
long-range memory process or just a consequence of non-linearity of Markov
processes. As our most recent result we discuss the long-range memory of the
order flow data in the financial markets and other social systems from the
perspective of the fractional L\`{e}vy stable motion. We test widely used
long-range memory estimators on discrete fractional L\`{e}vy stable motion
represented by the ARFIMA sample series. Our newly obtained results seem
indicate that new estimators of self-similarity and long-range memory for
analyzing systems with non-Gaussian distributions have to be developed.
