  Large amount of multidimensional data represented by multiway arrays or
tensors are prevalent in modern applications across various fields such as
chemometrics, genomics, physics, psychology, and signal processing. The
structural complexity of such data provides vast new opportunities for modeling
and analysis, but efficiently extracting information content from them, both
statistically and computationally, presents unique and fundamental challenges.
Addressing these challenges requires an interdisciplinary approach that brings
together tools and insights from statistics, optimization and numerical linear
algebra among other fields. Despite these hurdles, significant progress has
been made in the last decade. This review seeks to examine some of the key
advancements and identify common threads among them, under eight different
statistical settings.
