Searches for anomalous ionizing particles, strongly interacting massive particles (SIMPs, $\chi$), and magnetic monopoles by the ATLAS and CMS Collaborations with proton-proton collisions recorded at the Large Hadron Collider at a centre-of-mass energy of $\sqrt s$ = 13~TeV are presented. No evidence for such particles has been found, but
lepton-like multi-charged particles with masses between 50 GeV and 980 to 1220~GeV are excluded for electric charge numbers in the range $2 \leq z \leq 7$.
SIMP masses less than 100~GeV are excluded for a scalar mediator with couplings to quarks and SIMPs $g_q = 1$, $g_\chi = -1$.
An improvement by a factor five of the constraints on the direct production of magnetic monopoles with one or two magnetic Dirac charges and stable objects with $20 \leq z \leq 60$ was achieved with respect to a previous analysis, and the charge range has been extended to $60 \leq z \leq 100$.