Genderqueer is a catch-all term for gender identities

Gender identity

A gender identity is the way in which an individual self-identifies with a gender category, for example, as being either a man or a woman, or in some cases being neither, which can be distinct from biological sex. Basic gender identity is usually formed by age three and is extremely difficult to...

 other than man and woman, thus outside of the gender binary

Gender binary

The gender binary is the classification of sex and gender into two distinct and disconnected forms of masculine and feminine. It is one general type of a gender system. It can describe a social boundary that discourages people from crossing or mixing gender roles, or from creating other third ...

 and heteronormativity

Heteronormativity

Heteronormativity is a term invented in 1991 to describe any of a set of lifestyle norms that hold that people fall into distinct and complementary genders with natural roles in life. It also holds that heterosexuality is the normal sexual orientation, and states that sexual and marital relations...

. People who identify as genderqueer may think of themselves as one or more of the following:

• both man and woman (bigender
  Bigender
  Bigender, bi-gender or bi+gender describes a tendency to move between feminine and masculine gender-typed behaviour depending on context. Some bigendered individuals express a distinctly "en femme" persona and a distinctly "en homme" persona, feminine and masculine respectively; others have shades...
  
  , pangender
  Pangender
  Pangender is a term used to describe people who feel that they cannot be labeled as male or female in gender. As such it has a great deal of overlap with genderqueer. Pangender people feel that they do not fit into binary genders, instead identifying as mixed gender or as a third gendered...
  
  );
• neither man nor woman (genderless, agender);
• moving between genders (genderfluid);
• third gender
  Third gender
  The terms third gender and third sex describe individuals who are categorized as neither man nor woman, as well as the social category present in those societies who recognize three or more genders...
  
   or other-gendered; includes those who do not place a name to their gender;
• having an overlap of, or blurred lines between, gender identity and sexual orientation.

Some genderqueer people also identify as transgender

Transgender

Transgender is a general term applied to a variety of individuals, behaviors, and groups involving tendencies to vary from culturally conventional gender roles....

, and may or may not wish for physical modification or hormones to suit their preferred expression.