• Uncle: father's brother, mother's brother, father's/mother's sister's husband
• Aunt: father's sister, mother's sister, father's/mother's brother's wife
• Nephew: sister's son, brother's son, wife's brother's son, wife's sister's son, husband's brother's son, husband's sister's son
• Niece: sister's daughter, brother's daughter, wife's brother's daughter, wife's sister's daughter, husband's brother's daughter, husband's sister's daughter

When additional generations intervene (in other words, when one's collateral relatives belong to the same generation as one's grandparents or grandchildren), the prefix "grand" modifies these terms. (Although in casual usage in the USA a "grand aunt" is often referred to as a "great aunt", for instance.) And as with grandparents and grandchildren, as more generations intervene the prefix becomes "great grand", adding an additional "great" for each additional generation.

Most collateral relatives have never had membership of the nuclear family of the members of one's own nuclear family.

• Cousin: the most classificatory term; the children of aunts or uncles. One can further distinguish cousins by degrees of collaterality and by generation. Two persons of the same generation who share a grandparent count as "first cousins" (one degree of collaterality); if they share a great-grandparent they count as "second cousins" (two degrees of collaterality) and so on. If two persons share an ancestor, one as a grandchild and the other as a great-grandchild of that individual, then the two descendants class as "first cousins once removed" (removed by one generation); if the shared ancestor figures as the grandparent of one individual and the great-great-grandparent of the other, the individuals class as "first cousins twice removed" (removed by two generations), and so on. Similarly, if the shared ancestor figures as the great-grandparent of one person and the great-great-grandparent of the other, the individuals class as "second cousins once removed". Hence the phrase "third cousin once removed upwards".   

There is also an interesting chart.