The La Trobe Institute for Molecular Science (LIMS) was launched in 2009 as a state-of-the-art research hub dedicated to the study of molecular structures and processes fundamental to life. It was established with A$100 million in building funds from the Australian Government and La Trobe University. Professor Nick Hoogenraad served as the Institute's Director from its founding in 2009 until his retirement in 2014.  Professor Robert Pike served as Director of LIMS from 2015 to 2016. Professor Andrew Hill is the Institute's current director.

The Institute's newest building, LIMS1, was designed by Lyons Architects, who were appointed following a design competition sponsored by the Australian Institute of Architects. Construction began in August 2011, with an official sod turning presided by the Minister for Innovation, Industry, Science and Research, Senator Kim Carr. The building was officially opened in February 2013 by the Parliamentary Secretary for Higher Education and Skills, Ms Sharon Bird MP.

The LIMS1 building is a 11,000 square metre, six-storey, molecular sciences research hub containing 34 laboratories, with research, support and teaching facilities. It is interconnected with the LIMS2 building, an existing adjacent building, allowing co-location of research and support staff.

The building's lower levels accommodate undergraduate learning spaces, with open, flexible laboratories (accommodating up to 160 students) connected to "dry" teaching rooms. The top three levels of the building contains large interdisciplinary laboratories shared by multiple research teams.

The cellular facade features a chromosomal design that reflects the molecular research undertaken within the building. The complex has achieved formal certification for 5 Star Green Star (Design) using the Education Tool Version 1 through the Green Building Council of Australia.

Reko Rennie's 'Murri Totems' is located at the entrance of the LIMS building. The artwork consists of four 4.5 metre vertical structures incorporating the five platonic forms – icosahedron, octahedron, star tetrahedron, hexahedron and dodecahedron – and painted with Mr Rennie's traditional pattern.