  Some established and also novel techniques in the field of applications of
algorithmic (Kolmogorov) complexity currently co-exist for the first time and
are here reviewed, ranging from dominant ones such as statistical lossless
compression to newer approaches that advance, complement and also pose new
challenges and may exhibit their own limitations. Evidence suggesting that
these different methods complement each other for different regimes is
presented and despite their many challenges, some of these methods can be
better motivated by and better grounded in the principles of algorithmic
information theory. It will be explained how different approaches to
algorithmic complexity can explore the relaxation of different necessary and
sufficient conditions in their pursuit of numerical applicability, with some of
these approaches entailing greater risks than others in exchange for greater
relevance. We conclude with a discussion of possible directions that may or
should be taken into consideration to advance the field and encourage
methodological innovation, but more importantly, to contribute to scientific
discovery. This paper also serves as a rebuttal of claims made in a previously
published minireview by another author, and offers an alternative account.
