By Miri –
Like most other religions, Judaism is not one static homogeneous belief system. Throughout its history, and throughout the various places that Jews took their beliefs, their practices and culture to, Judaism has changed and developed. From an analytic point of view it may be actually more appropriate to view Judaism as an umbrella term for a lot of very different strands and movements. 
In the following I will attempt to trace back the history of the denominational structure of those movements within Judaism that grew out of the Jewish reform movement and that from this point departed from Orthodox or traditional Jewish thought.  
From Enlightenment and Jewish Emancipation Towards Reform Judaism 
The move away from orthodox Judaism is commonly associated with the Jewish Enlightenment, or Haskalah (Hebrew: enlightenment), a movement that originated in Germany in the 19th century and advocated a “coming out of the ghettos”, i.e. the integration of the Jewish communities into European society. 
In opposition to traditional Jewish scholarship and by seeking modernised philosophical and critical revision within Jewish belief and lifestyle, the Haskalah aimed at adapting Judaism to contemporary European life. The movement that soon spread throughout Europe, succeeded in creating a secular Jewish culture, which emphasised Jewish history and identity, rather than religion. It also influenced and aided the emergence of Jewish political movements striving for emancipation and later also for a Jewish homeland, i.e. Zionism. 

Regina Jonas, first woman to be ordained as Rabbi, Germany, 1935

The Haskalah had however also non-intended side-effects as it contributed to the assimilation of European Jewry and a concomitant demise in Jewish education. In response to that, in the early 19th century another movement of Jewish educators, scholars and rabbis emerged, later to be referred to as the German Reform movement, which sought to modernise Judaism. 
Many of the ideas that were already brought up by the Haskalah, such as the move away from law and obedience to love and community as the defining features of religion, figured prominently in the debates of the reform movement. While many proponents of the movement had no interest in forming separate congregations, the discussions that were stirred during those times ultimately led to a wider diversification and to the emergence of different denominations within Judaism. 
Reform Judaism is by now often used interchangeably with Progressive Judaism and both often act as umbrella terms for various forms of Judaism that grew out of the reform movement. In the U.S. Reform Judaism still constitutes its own denomination which is at the same time the largest one with an estimated 1,5 million members. In many parts of Europe the term Liberal Judaism is also often used. 
In Israel the reform movement is usually referred to as Progressive Judaism. As opposed to their counterparts in the rest of the world, Israeli Reform Judaism has been fighting a much harder struggle for acceptance and it was only in May 2012 that their rabbis would officially be recognised by the state and started to receive state funding just like Orthodox rabbis, a notion that was celebrated as a major breakthrough in terms of equalising the different Jewish streams in Israel.

From Positive-Historical Judaism to Conservative Judaism 

Many rabbis and Jewish scholars agreed with the Haskalah and the reform movement that Jewish orthodoxy in its current form could and should not be upheld, however, many were also opposed to the radicalism inherent to the ideas and reforms of Reform Judaism.
Rabbi Zacharias Frankel, founder of what is now considered Positive-Historical Judaism, maintained that the Halakha, the central principle of Jewish tradition, must be followed, but should be viewed as entailing human, historical and dynamic elements, which thus facilitate change and development. This stream of thought which came to form the basis of conservative Jewish reasoning also already explains the term “conservative”, which does not imply an adherence to political conservatism, but highlights instead the conviction that Jews should conserve tradition, rather than reform or abandon it. Due to the potential conflation of the term with political conservatism, the movement is often also referred to as Masorti (Hebrew for “traditional”) Judaism.

A young girl reading from the Torah for her Bat-Mitzvah

Conservative or Masorti Judaism flourished especially in the US, where it soon became the largest Jewish denomination, and was only recently superseded by Reform Judaism. Up until today Conservative Judaism maintains its dynamic view of the Halakha and keeps on introducing new interpretations and changes. Particularly its view on gender issues has led to controversies and to yet another split within the denomination and hence to the foundation of the Union for Traditional Judaism.
The most important changes regarding gender issues include the counting of women in the Minyan, the quorum of ten Jewish adults required for certain religious obligation including public prayer, the admission of women to Rabbinical and Cantorial school and more recently the ordination of gay and lesbian rabbis, as well as the permission of same-sex marriage.

In Israel Conservative Judaism constitutes a rather small movement, counting approximately 50,000 members, most of which are immigrants from the U.S. Just like Reform Judaism, Conservative Judaism was until recently disadvantaged by the Israeli government, which used to only recognise and fun Orthodox institutions. 

Reconstructionist Judaism  

Another branch of Judaism that originated from Conservative Judaism is the Reconstructionist Movement, which developed mainly between the late 1920s to 1940s and founded its first Rabbinical college in 1968 in the U.S..
Following the movements’ founder Mordecai Kaplan, Judaism is understood as a progressively evolving civilisation, which should be interpreted within the context of contemporary life, without abandoning its traditional values. Believing in the human authorship of all religious traditions, including their own, the Halakha is not seen as an absolute binding set of commandments, but should be adapted to social conditions, political changes, and cultural influences. Reconstructionist Judaism is therefore a bottom-up approach, which starts with the experiences of the Jewish people and not with god, who should rather be seen as “the sum of all natural processes that allow man [sic] to become self-fulfilled”.

“To believe in God means to accept life on the assumption that it harbors conditions in the outer world and drives in the human spirit which together impel man to transcend himself. To believe in God means to take for granted that it is man’s destiny to rise above the brute and to eliminate all forms of violence and exploitation from human society. In brief, God is the Power in the cosmos that gives human life the direction that enables the human being to reflect the image of God.” 

Jewish lesbian wedding, California

With their humanist approach, reconstructionists believe that all peoples are called to build a world of justice and compassion. The absolute equality of men and women is therefore one of the movement’s central tenets and women were ordained from the beginning. As opposed to most other denominations, the reconstructionists, together with Reform Judaism, include patrilineal descent, i.e. the acceptance of children of Jewish fathers as Jews and also warmly welcomes mixed marriages. The reconstructionists have also a long history in supporting both LGBTQ civil rights, as well as the inclusion of LGBTQ people in all aspects of Jewish life.

The Reconstructionist Movement is still a rather small branch of Judaism and its communities are mainly, though not exclusively, found in the U.S. and Canada.