  The $P_c(4380)^+$ and $P_c(4450)^+$ states recently discovered at LHCb have
masses close to several relevant thresholds, which suggests they can be
described in terms of meson-baryon degrees of freedom. This article explores
the phenomenology of these states, and their possible partners, from this point
of view. Competing models can be distinguished by the masses of the neutral
partners which have yet to be observed, and the existence or otherwise of
further partners with different isospin, spin, and parity. Future experimental
studies in different decay channels can also discriminate among models, using
selection rules and algebraic relations among decays. Among the several
possible meson-baryon pairs which could be important, one implies that the
states are mixtures of isospins 1/2 and 3/2, with characteristic signatures in
production and decay. A previous experimental study of a Cabibbo-suppressed
decay showed no evidence for the states, and further analysis is required to
establish the significance of this non-observation. Several intriguing
similarities suggest that $P_c(4450)^+$ is related to the $X(3872)$ meson.
