Although incredibly rapid, kittens do indeed undergo a teething phase. This period usually begins at between ten weeks to six months of age and tends to be uncomfortable. To go into greater detail, a kitten's primary incisors are replaced by thirty permanent teeth that will see them through adulthood and (hopefully) their senior years.
If you notice your kitten drooling or turning down their food during this time period, don't worry. After all, their adult tooth buds are moving though bones and erupting through their gums – it's bound to be an uncomfortable time for them!