For elements in the main groups of the periodic table, the valence can vary between 1 and 8.
Many elements have a common valence related to their position in the periodic table, and nowadays this is rationalised by the octet rule.
The Greek/Latin numeral prefixes (mono-/uni-, di-/bi-, tri-/ter-, and so on) are used to describe ions in the charge states 1, 2, 3, and so on, respectively. Polyvalence or multivalence refers to species that are not restricted to a specific number of valence bonds. Species with a single charge are univalent (monovalent). For example, the  cation is a univalent or monovalent cation, whereas the  cation is a divalent cation, and the  cation is a trivalent cation. Unlike Cs and Ca, Fe can also exist in other charge states, notably 2+ and 4+, and is thus known as a multivalent (polyvalent) ion. Transition metals and metals to the right are typically multivalent but there is no simple pattern predicting their valency.
† The same adjectives are also used in medicine to refer to vaccine valence, with the slight difference that in the latter sense, quadri- is more common than tetra-.
‡ As demonstrated by hit counts in Google web search and Google Books search corpora (accessed 2017).
§ A few other forms can be found in large English-language corpora (for example, *quintavalent, *quintivalent, *decivalent), but they are not the conventionally established forms in English and thus are not entered in major dictionaries.