There are many groups and individuals below is a collection of practitioners who are engaged in social impact and/or humanitarian architecture.

European based groups

51N4E
amid.cero.9
Anna Heringer 
APractice
Architecture00
Architects for Social Housing
ASA
Atelier D’Architecture Autogeree
AWP
Dogma
Funkia
Ecosistema Urbano
EEEstudio 
Emergency Architecture & Human Rights
Forensic Architecture
Freiraum Kollektive
Guerrilla Architects
HATprojects
Hollmen Reuter Sandman
InBetween Economies 
Kere Architecture 
La Rivoluzione Delle Seppie
Made in Earth
MUF
New South
NLE
Raumlabor 
Recetas Urbanas
Studio Weave
Territorial Agency
Tomorrows Thoughts Today
Urban Think Tank 
URBIO
ZUS
Exyzt
Something's Fantastic


Transnational
MADE Collective
Collective Disaster

US based organizations
Architecture for Humanity (1999-2015) // Architecture for Humanity UK still in operation.
Asian Neighborhood Design
Association for Community Design
buldingcommunityWorkshop (bcWorkshop)
Campus Compact
Center for Resilient Design
Cleveland Urban Design Collaborative (CUDC)
Community Design Collaborative of Philadelphia
Community Design Center of Pittsburgh
Democracy Collaborative
Design Corps
Detroit Collaborative Design Center (DCDC)
Enterprise Community Partners - Rose Architectural Fellowship Program
Environmental Design Research Association
Imagining America
Miami University Center for Community Engagement in Over-the-Rhine
National Charrette Institute
Neighborhood Design Center in Baltimore
North Carolina State University Community Design + Planning
Pratt Institute Center for Community Development
Public Architecture
The Rural Studio
Studio 804 University of Kansas
University of San Francisco Architecture and Community Design Program Department of Art + Architecture
University of South Florida
University of Washington Howard S.Wright Neighborhood Design/Build Studio

Writers
Keefer Dunn

Books
Activism in Architecture // Margot McDonald
Architecture Activism // GRAFT
Design Like You Give A Damn: Architectural Responses to Humanitarian Crises
Design Like You Give A Damn 2: Building Change From the Ground Up
Expanding Architecture
When Architecture Meets Activism // Roger Guy