  In this paper we study aspects of top tagging from first principles of QCD.
We find that the method known as the CMS top tagger becomes collinear unsafe at
high $p_t$ and propose variants thereof which are IRC safe, and hence suitable
for analytical studies, while giving a comparable performance to the CMS
tagger. We also develop new techniques to identify three-pronged jet
substructure, based on adaptations of the Y-splitter method and its combination
with grooming. A novel feature of our studies, relative to previous
calculations of two-pronged substructure, is our use of triple-collinear
splitting functions, which owes to the presence of two mass scales of the same
order, $m_t$ and $m_W$, in the signal jet. We carry out leading logarithmic
resummed calculations for the various top-taggers, for both background and
signal jets, and compare the results to those from parton showers. We also
identify and comment on the main features driving tagger performance at high
$p_t$ and discuss the role of non-perturbative effects.
