Saudade (English: /saʊˈdɑːdə/; plural saudades) is a word in Portuguese and Galician denoting an emotional state of melancholic or profoundly nostalgic longing for a beloved yet absent someone or something. It derives from the Latin word for solitude. It is often associated with a repressed understanding that one might never encounter the object of longing ever again. It is a recollection of feelings, experiences, places, or events, often elusive, that cause a sense of separation from the exciting, pleasant, or joyous sensations they once caused. Duarte Nunes Leão defines saudade as, "Memory of something with a desire for it". In Brazil, the day of saudade is officially celebrated on 30 January. It is not a widely acknowledged day in Portugal.

Saudade ultimately derives from the Latin solitās, solitātis, meaning "solitude". The word saudade was used in the Cancioneiro da Ajuda (13th century), in the Cancioneiro da Vaticana and by poets of the time of King Denis of Portugal (reigned 1279–1325). Some specialists argue that the word may have originated during the Great Portuguese Discoveries, expressing and giving meaning to the sadness felt about those who departed on journeys to unknown seas and often disappeared in shipwrecks, died in battle, or simply never returned. Those who stayed behind—mostly women and children—suffered deeply in their absence. However, Portuguese discoveries started in 1415 and the word has been found in earlier texts. The Reconquista may also offer a plausible genesis.^{[citation needed]}

The state of mind has subsequently become a "Portuguese way of life": a constant feeling of absence, the sadness of something that's missing, wistful longing for completeness or wholeness and the yearning for the return of what is now gone, a desire for presence as opposed to absence—as it is said in Portuguese, a strong desire to matar as saudades (lit. 'to kill the saudades').

In the latter half of the 20th century, saudade became associated with the longing for one's homeland, as hundreds of thousands of Portuguese-speaking people left in search of better futures in South America, North America, and Western Europe. Besides the implications derived from a wave of emigration trend from the motherland, historically speaking saudade is the term associated with the decline of Portugal's role in world politics and trade. During the so-called "Golden Age", synonymous with the era of discovery, Portugal rose to the status of a world power, and its monarchy became the richest in Europe and one of the richest global empires in history. But with the competition from other European nations, the country went both colonially and economically into a prolonged period of decay. This period of decline and resignation from the world's cultural coincides with the cultural rising of saudade in Portuguese society.

The Dicionário Houaiss da Língua Portuguesa defines saudade (or saudades) as "A somewhat melancholic feeling of incompleteness. It is related to thinking back on situations of privation due to the absence of someone or something, to move away from a place or thing, or to the absence of a set of particular and desirable experiences and pleasures once lived."

The dictionary from the Royal Galician Academy, on the other hand, defines saudade as an "intimate feeling and mood caused by the longing for something absent that is being missed. This can take different aspects, from concrete realities (a loved one, a friend, the motherland, the homeland...) to the mysterious and transcendent. It is quite prevalent and characteristic of the Galician-Portuguese world, but it can also be found in other cultures."

Saudade is a word in Portuguese and Galician that claims no direct translation in English. However, a close translation in English would be "desiderium." Desiderium is defined as an ardent desire or longing, especially a feeling of loss or grief for something lost. Desiderium comes from the word desiderare, meaning to long for. Connections between desiderium and nostalgia have also been drawn; the former can be seen as expressing the latter for things that can't be experienced any more, or things that someone may have never experienced themselves.

In Portuguese, "Tenho saudades tuas" or "Estou com saudades de ti/você" translates as "I have (feel) saudade of you" meaning "I miss you", but carries a much stronger tone. In fact, one can have saudade of someone whom one is with, but have some feeling of loss towards the past or the future. For example, one can have "saudade" towards part of the relationship or emotions once experienced for/with someone, though the person in question is still part of one's life, as in "Tenho saudade do que fomos" (I feel "saudade" of the way we were). Another example can illustrate this use of the word saudade: "Que saudade!" indicating a general feeling of longing, whereby the object of longing can be a general and undefined entity/occasion/person/group/period etc. This feeling of longing can be accompanied or better described by an abstract will to be where the object of longing is.