  Strong monads are important for several applications, in particular, in the
denotational semantics of effectful languages, where strength is needed to
sequence computations that have free variables. Strength is non-trivial: it can
be difficult to determine whether a monad has any strength at all, and monads
can be strong in multiple ways. We therefore review some of the most important
known facts about strength and prove some new ones. In particular, we present a
number of equivalent characterizations of strong functor and strong monad, and
give some conditions that guarantee existence or uniqueness of strengths. We
look at strength from three different perspectives: actions of a monoidal
category V, enrichment over V, and powering over V. We are primarily motivated
by semantics of effects, but the results are also useful in other contexts.
