Teacups - refers to dogs that as adults weigh only about 7 to 10 pounds. Any breed can be miniaturized - but most commonly I see Yorkies, Maltese, Pomeranians, Poodles, Chihuahuas, Papillons, Mikis, Havanese, and other so-called toy breeds. They are so cute but - not without their own health problems. People interested in any breed must do some research and find out what if any health issues that type of dog possesses.
Tiny dogs because of the extreme breeding required to obtain their miniature size may harbor a variety of genetic health problems. They often have bad mouths with bad occlusion resulting in overbites, underbites, bad teeth and poor dentition. This can require considerable dental care during their lives. Also, orthopedic problems are not uncommon. Knee problems - luxating patellas - ( dislocating knee caps ) are very common, intervertebral disc disease, and fractures because they are so fragile are likewise very common. Collapsing trachea , allergies, and asthma have been recorded for these breeds. Neurological problems with problems stemming from open fontanelles, hydrocephalus, and skull malformations with their "bubble heads," particularly in Chihuahuas. These breeds are prone to bladder stones, umbilical hernias, and may show hip problems. Furthermore, most of these breeds show a high percentage for the need for C-sections. Young males in these tiny breeds often are born with retained testicles. Many teacup breeds are often born with heart murmurs as well.
Before you decide on any breed / do your homework. Talk to your veterinarian, people that have that breed, breeders - and decide if a teacup breed is right for you. Your veterinarian can help answer your questions.