  In this review we summarize theoretical progress in the field of active
matter, placing it in the context of recent experiments. Our approach offers a
unified framework for the mechanical and statistical properties of living
matter: biofilaments and molecular motors in vitro or in vivo, collections of
motile microorganisms, animal flocks, and chemical or mechanical imitations. A
major goal of the review is to integrate the several approaches proposed in the
literature, from semi-microscopic to phenomenological. In particular, we first
consider "dry" systems, defined as those where momentum is not conserved due to
friction with a substrate or an embedding porous medium, and clarify the
differences and similarities between two types of orientationally ordered
states, the nematic and the polar. We then consider the active hydrodynamics of
a suspension, and relate as well as contrast it with the dry case. We further
highlight various large-scale instabilities of these nonequilibrium states of
matter. We discuss and connect various semi-microscopic derivations of the
continuum theory, highlighting the unifying and generic nature of the continuum
model. Throughout the review, we discuss the experimental relevance of these
theories for describing bacterial swarms and suspensions, the cytoskeleton of
living cells, and vibrated granular materials. We suggest promising extensions
towards greater realism in specific contexts from cell biology to ethology, and
remark on some exotic active-matter analogues. Lastly, we summarize the outlook
for a quantitative understanding of active matter, through the interplay of
detailed theory with controlled experiments on simplified systems, with living
or artificial constituents.
