Housing First is a model for treatment of people experiencing homelessness, especially chronic homelessness (cumulatively over a year, and involving a disability), with psychiatric disorders and/or substance disorders. It was developed and named in the U.S. in the late 1980s and early 1990s, and has become adopted as a best practice in many countries.
Housing First is considered an alternative to -- and was originally and is often described by contrast to -- traditional systems of emergency shelter / transitional housing progression, or "housing readiness" models. In these approaches, individuals are expected (or required) to pass through different 'levels' of housing, and often required treament or assistance programs, whereby each level moves them closer to 'independent' or permanent housing: for example, from the streets to a public shelter, and from a public shelter to a transitional housing program, and from there to their own apartment in the community. Housing First approaches typically aim to move the homeless individual or household from the streets or shelters directly into into permanent housing, meaning that there is no time limit to their residence, or other conditions except for normal residential lease terms. (by US Department of Housing and Urban Development definition of "permanent housing," the housing tenure also must not have eviction except for cause, which is a tenant protection that most rental housing in the US does not have).
Housing First approaches are based on the concept that a homeless individual or household's first and primary need is to obtain stable housing, and that other issues that may affect the household can and should be addressed once housing is obtained. Also, that other issues such as substance abuse, re-employment, medical treatment, are often very difficult to address in the absence of stable housing.
In contrast, predecessor programs often implicitly or explicitly follow a model described as 'housing readiness' — that is, that an individual or household must address other issues that may have led to the episode of homelessness prior to entering housing."
--adapted from Wikipedia, "Housing First."
Limitations and critical questions
('TAU' means "Treatment as Usual." In the context of Housing First studies, it typically means, "housing readiness" approaches, or whatever happens with patients usually in the locality where study was conducted).
[Baxter et al 2019]:
"the data included in this review were exclusively from North America and the participants were all selected on the basis of complex health needs (such as mental illness, substance abuse or chronic physical illness) as per the principles of HF.16 17 This may limit the generalisability of our findings internationally, as well as to homeless people without complex health needs."
"Our systematic review found that HF resulted in large improvements in housing stability; with unclear short-term impact on health and well-being outcomes. For mental health, quality of life and substance use, no clear differences were seen when compared with TAU [Treatment As Usual].. HF participants showed a clear reduction in non-routine use of healthcare services, over TAU. This may be an indicator of improvements in health."
"Housing First approaches do not appear to consistently improve or harm health in the short-term, but long-term impacts are unknown."
Cost / spending outcomes 
from December, 2016 literature review and commentary [Kertesz et al 2016]:
"Advocates for ending homelessness have increasingly turned to a financial argument, claiming that permanent supportive housing will deliver net cost savings to society." "
We believe the cost-savings argument is problematic and that it would be better to reframe the discussion to focus primarily on the best way to meet this population’s needs."
"Higher-quality randomized, controlled trials...haven’t demonstrated net cost savings." "Staking the future of Housing First on the expectation that it will save money could undermine efforts to deliver an effective intervention to the majority of the population it’s intended to serve."
- Baxter AJ, Tweed EJ, Katikireddi SV, et al [Baxter 2019]. "Effects of Housing First approaches on health and well-being of adults who are homeless or at risk of homelessness: systematic review and meta-analysis of randomised controlled trials." J Epidemiol Community Health 2019;73:379-387.
- Canadian Observatory on Homelessness (COH). “Canadian Definition of Homelessness.” 2012, revised 2017.
- Corinth, K., 2017. “The impact of permanent supportive housing on homeless populations.”
Journal of Housing Economics 35: 69–84.
- Council of Economic Advisers. "The State of Homelessness in America." September 2019. https://www.whitehouse.gov/wp-content/uploads/2019/09/The-State-of-Homelessness-in-America.pdf.
- Evans, William N., David C. Philips, and Krista J. Ruffini. [Evans 2019] "Reducing and Preventing Homelessness: A Review of the Evidence and Charting a Research Agenda." Abdul Latif Jameel Poverty Action Lab / NBER Working Paper 26232, September 2019. http://www.nber.org/papers/w26232; https://drive.google.com/file/d/1sJ5FSfrtx5YE0i_AuacH7Yz_JNMOIfRn/view?usp=drivesdk.
- Goodman, S., P. Messeri, and B. O’Flaherty. 2017. “Homelessness prevention in New York City:
On average, it works.” Journal of Housing Economics 31: 14–34.
- Kertesz, S. G., and G. Johnson. 2017. “Housing First: Lessons from the United States and Challenges for Australia.” Australian Economic Review 50, no. 2: 220–28
- Kertesz, Stefan G. Kertesz, M.D., Travis P. Baggett, M.D., M.P.H., James J. O’Connell, M.D., David S. Buck, M.D., M.P.H., and Margot B. Kushel, M.D. "Permanent Supportive Housing for Homeless People — Reframing the Debate." New England Journal of Medicine 2016; 375:(article). https://dx.doi.org/10.1056/NEJMp1608326. Full text.
- Lucas, D. S. 2017. “The impact of federal homelessness funding on homelessness.” Southern Economic Journal 84, no. 2: 548–76.
"Federal spending on homelessness has increased significantly in recent years. I estimate the relationship between federal homelessness funding and homeless counts in 2011, 2013, and 2015 cross sections. I instrument for funding using a community’s pre-1940 housing share, a key variable in an originally unrelated funding formula borrowed for homelessness grants. Funding increases sheltered homelessness; meanwhile, funding is unrelated to unsheltered homelessness. Lower bound estimates suggest that the minimum cost of reducing unsheltered homelessness has increased over time, from $16,400 in 2011 to $20,800 in 2013 to $50,000 in 2015. In 2013, an additional $1 thousand dollars corresponds to a .309 higher homeless rate per 10,000 people. The effect is larger for families than individuals. Funding is positively related to chronic homelessness and is unrelated to youth and child homelessness. My results suggest limitations on federal funding’s ability to reduce homelessness among some of the most marginalized groups in society."
- Ly, A., and E. Latimer. 2015. “Housing first impact on costs and associated costs offsets: A review of the literature.” Canadian Journal of Psychiatry 60, no. 11: 475–87.
- Moulton, S. 2013. “Does increased funding for homeless programs reduce chronic
homelessness?” Southern Economic Journal 79, no. 3: 600–20.
- O’Flaherty, Brendan. 2019. “Homelessness Research: A Guide for Economists (and Friends).” Journal of Housing Economics 44 (2019): 1–25. https://doi.org/10.1016/j.jhe.2019.01.003. Accepted manuscript: .