Recent measurements of charmless $b$-hadron decays using 3\,fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=7$ and $8$\,TeV, collected by the LHCb experiment, are presented.

A search is performed for $\Lambda_{b}$ and $\Xi_{b}^{0}$ decays to $\Lambda h^{+}h^{\prime -}$ final states.

The decays $\Lambda_{b} \to \Lambda K^{+}\pi^{-}$ and $\Lambda_{b} \to \Lambda K^{+}K^{-}$ are observed for the first time, and their branching fractions and $CP$ asymmetries are measured.

Evidence is seen for the $\Lambda_{b} \to \Lambda \pi^{+}\pi^{-}$ channel, and limits are set on the branching fractions of the $\Xi_{b}^{0} \to \Lambda h^{+}h^{\prime -}$ decay modes.

The decay $\Lambda_{b} \to \Lambda \phi$ is observed for the first time, and its branching fraction and $T$-odd triple-product asymmetries are measured.

A search is performed for the decay $B_{c}^{+} \to p \bar{p} \pi^{+}$.

No signal is found, and an upper limit is set on the product of the branching fraction with the ratio of $B_{c}^{+}$ and $B^{+}$ production cross-sections.