Ever since the one child policy, most newborns will not have any brothers or sisters, therefore your kids will not have aunts and uncles. That is why it is so shocking for foreigners learning Chinese to discover that while many do not have actual brothers, sisters, cousins, or uncles, they do have many words for the different family members. Did you know that there are different names for grandmothers and grandfathers depending on the side of the family they are from?
The Chinese used to believe that when a girl marries, her kids belong the the family of the husband, not hers, therefore the words for grandmother and grandfather are different for the mother's and father's side. For example, one can call granddad (father's father) 祖父 (zǔfù) or 爷爷 (yéye), and grandma (father's mother) 祖母 (zǔmǔ) or 奶奶 (nǎinɑi) while the mother's parents have the word 外(wài) added, which is literally translated to "outside". So the mother's parents will be called 外祖父 (wàizǔfù) or 外公 (wàiɡōnɡ) for grandfather, and 外祖母 (wàizǔmǔ) or 外婆 (wàipó) for grandmother.
The words to describe the family connection not only distinguish the difference between the mother's and father's side, but also distinguish seniority. The words can show if that person is older or younger than you/your parents. While most foreigners know the difference between siblings like elder brother 哥哥 (ɡēɡē), younger brother 弟弟 (dìdi), elder sister 姐姐 (jiějie), younger sister 妹妹 (mèimei), there are more words that distinguish if they are older aunts and uncles (older than you parents) or the younger ones. For example: the father's elder brother is called 伯父 (bófù), while his younger brother is called 叔叔 (shūshu). The father's older sister is 大姑 (dàɡu) and younger sister is 姑姑 (ɡūgu). The mother's brother is 舅父 (jiùfù) or more commonly 舅舅 (jiùjiu), her sister is called 姨妈 (yímā) or 姨母 (yímǔ). Strangely there is no difference between mother's older or younger siblings.
Confused yet? Well there's more. Chinese family titles describe the mother's or father's side of the family, describe whether they are the older or younger sibling, and they even let you know if the aunt/uncle is related to you by blood, or by law. This is why you cannot just call your father's brother's wife "aunt". There are certain differences, for example: your father's elder brother's wife is called 伯母 (bómǔ), his little brother's wife is 婶婶 (shěnshěn), mother's sister-in-law will be 舅妈 (jiùmā) and mother's brother-in-law will be 姨丈 (yízhànɡ) or 姨夫 (yífù).
The difference between cousins is not that big. While cousins from the paternal side are 堂哥 (tánɡɡē) for a male older cousin and 堂弟 (tánɡdì) for a male younger cousin, 堂姐 (tánɡjiě) stands for female older cousin, while 堂妹 (tánɡmèi) stands for female younger cousin. Cousins from the maternal side are called 表哥 (biǎogē) for an older male cousin, 表弟 (biǎodì) for a younger male cousin, 表姐 (biǎojiě) is an older female cousin and 表妹 (biǎomèi) is for a younger female cousin. There is one exception to the rule above, if your father has a sister, then her children follow the naming system for the maternal cousins.
For grandparents the rules apply as well. Your son's kids are indeed YOUR grandchildren, but your daughter's kids are not really (because they belong to the paternal side). Your grandson is 孙子(sūnzi), granddaughter is 孙女 (sūnnǚ), while your daughter's children have the word 外 (wài) added; grandson is 外孙 (wàisūn), and granddaughter is 外孙女 (wàisūnnǚ). Your son-in-law is called 女婿 (nǚxù) and daughter-in-law is called 儿媳 (érxí).
For those of you with nephews and nieces, unfortunately, they have different names as well. For instance your brother's kids are called 侄子(zhízi) for males, and 侄女 (zhínǚ) for females. Your sister's son is called 外甥 (wàishēnɡ) and her daughter is 外甥女 (wàishēnɡnǚ).