The electrophilic addition of hydrogen halides to alkynes, also called polar hydrohalogenation of alkynes, is one of the most classical and important organic reactions. Mechanistic and stereoselective insights into the hydrohalogenation of various structurally different distinct alkynes, including both alkyl and aryl substituted acetylenes, in acetic acid were investigated theoretically via density functional theory (DFT) calculations. The results indicate that π-complexes between hydrogen halides and alkynes are first formed, and then all alkynes can undergo a competitive bimolecular intimate ion-pair syn-addition process and a pentamolecular concerted anti-addition process through the cyclic proton transfer mechanism for proton transfer in the absence of tetraalkylammonium halides or a termolecular electrophilic addition (AdE3) process in the presence of tetraalkylammonium halides. All aliphatic alkynes undergo slightly to obviously predominant anti-addition in hydrohalogenations both in the absence and presence of tetraalkylammonium halides. Aromatic 1-arylalk-1-ynes favour syn-additions through bimolecular intimate ion-pair processes with asynchronous concerted characteristics in the absence of tetraalkylammonium halides, while most of them generally prefer anti-addition in the presence of tetraalkylammonium halides. The stereoselectivity is significantly affected by both the electronic and steric effects of 1-arylalk-1-ynes and halides in the reaction mixture. Strongly electron-rich and bulky 1-arylalk-1-ynes generally favour syn-addition in the presence of tetraalkylammonium halides, especially arylethynes in hydrochlorination. Anti-Markovnikov hydrohalogenations of 1-arylalk-1-ynes also prefer anti-addition both in the absence and presence of tetraalkylammonium halides even in small amounts due to high activation energies. The current investigation provides deep insights into the mechanism and stereoselectivity in polar hydrohalogenations of alkynes.