New Zealand had a bicameral system from the early days of colonisation, starting in the mid nineteenth century. Originally the members of the Legislative Council (upper house, NZLC from now)were selected by the Governor of the day (the Queen's representative, and a role which correlates to the modern Governor-General) and had life appointments. The governors saw a gradual diminishing of power as the parliament of the country became more used to running political processes and exerting control. By the 1870s the Governor could be out manoeuvred by parliament and the Premiers began to recommend appointments to the NZLC. These appointments meant that the members were usually representative of the government of the day, and as their role was to scrutinise legislation passed by the lower house, the role was... debatable in its necessity.

In the late 1800s frustrations with the NZLC arose with Premiers having to contend with passing legislation. First it would go through the lower house which they controlled, and then through the upper house, which was controlled by the life appointments of the previous Premier. Law was passed to make appointments a seven year term, effectively curtailing the last remaining obstacle to legislation passing. The seven year term meant you could be relatively sure of having friendly votes in the NZLC.

By the 1940s the view was that the NZLC was an unnecessary aspect of parliament. It had no function except to approve legislation that came from the lower house, which was often coming from a party which had selected the members of the upper house. It was like having a vote on the best sports team and then only asking fans of your team to vote.

The NZLC was abolished in an interesting way. Legislation had to be passed that came directly from Westminster, enabling the abolition of a key part of the Westminster system. Once that was done, the Prime Minister of the day, Sidney Holland, nominated a group of members to the NZLC. They were known as the Suicide Squad. This was because the abolition of the LC required its members to vote to abolish it. Those members were volunteers, with several ex-MPs among them, who were elected, then promptly called a vote and voted to end the system.

The unicameral system has existed since, but there are occasional calls for us to re-add an upper house. It's not a strongly supported view, and I've not heard about it for a few years now. I'm also not entirely sure what the benefit would be, so I don't see it gaining any traction soon.