  With the broader and highly successful usage of machine learning in industry
and the sciences, there has been a growing demand for Explainable AI.
Interpretability and explanation methods for gaining a better understanding
about the problem solving abilities and strategies of nonlinear Machine
Learning, in particular, deep neural networks, are therefore receiving
increased attention. In this work we aim to (1) provide a timely overview of
this active emerging field, with a focus on 'post-hoc' explanations, and
explain its theoretical foundations, (2) put interpretability algorithms to a
test both from a theory and comparative evaluation perspective using extensive
simulations, (3) outline best practice aspects i.e. how to best include
interpretation methods into the standard usage of machine learning and (4)
demonstrate successful usage of explainable AI in a representative selection of
application scenarios. Finally, we discuss challenges and possible future
directions of this exciting foundational field of machine learning.

Machine Learning;Artificial Intelligence;Computer Vision and Pattern Recognition;Neural and Evolutionary Computing;Machine Learning