Belief is assent to a proposition:

Belief in the psychological sense, is a representational mental state that takes the form of a propositional attitude. In the religious sense, "belief" refers to a part of a wider spiritual or moral foundation, generally called faith.

Belief is considered propositional in that it is an assertion, claim or expectation about reality that is presumed to be either true or false (even if this cannot be practically determined, such as a belief in the existence of a particular deity). Historically, philosophical attempts to analyze the nature of belief have been couched in terms of judgement. David Hume and Immanuel Kant are both particularly well known for their analyses using this framework.

Belief, knowledge and epistemology:

Knowledge is often defined as justified true belief, in that the belief must be considered to correspond to reality and must be derived from valid evidence and arguments. However, this definition has been challenged by the Gettier problem which suggests that justified true belief does not provide a complete picture of knowledge.

To believe something can be interpreted as assigning a probability of more than 50% that something is true. The rule of the thumb from a school of epistemology that says that certainty should be as big as the corresponding evidence is called evidentialism.

Is belief voluntary?

Most philosophers hold the view that belief formation is to some extent spontaneous and involuntary. Some people think that one can choose to investigate and research a matter but that one can not choose to believe. On the other hand, most people have the impression that in some cases people don't believe things because they don't want to believe, especially about a matter in which they are emotionally involved.

Delusional beliefs:

Delusions are defined as beliefs in psychiatric diagnostic criteria (for example in the DSM). Psychiatrist and historian German Berrios has challenged the view that delusions are genuine beliefs and instead labels them as "empty speech acts", where affected persons are motivated to express false or bizarre belief statements due to an underlying psychological disturbance. However, the majority of mental health professionals and researchers treat delusions as if they were genuine beliefs.

Read more about the "Belief as Psychological Theory".