The performance of taggers for hadronically decaying top quarks and $W$ bosons in $pp$ collisions at $s$ = 13 TeV recorded by the ATLAS experiment at the Large Hadron Collider is presented. A set of techniques based on jet shape observables are studied to determine a set of optimal cut-based taggers for use in physics analyses. The studies are extended to assess the utility of combinations of substructure observables as a multivariate tagger using boosted decision trees or deep neural networks in comparison with taggers based on two-variable combinations. In addition, for highly boosted top-quark tagging, a deep neural network based on jet constituent inputs as well as a re-optimisation of the shower deconstruction technique is presented. The performance of these taggers is studied in data collected during 2015 and 2016 corresponding to 36.1 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ for the $tt¯$ and $\gamma +$jet and 36.7 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ for the dijet event topologies.