Hurricane Harvey might have you wondering who is supposed to do what when there is a disaster. Here's is a very very simplified explanation.
Emergency management encompasses not just emergency managers. TONS of people and agencies at all levels are involved in doing emergency management work - whether they call it that or not. The vast number of people involved in emergency management can be confusing. Who is supposed to be doing what and when?
The primary people responsible for emergency management is the community that is experiencing the disaster. Day to day they're most responsible for overseeing preparedness and mitigation efforts, planning for or doing recovery work, and responding to the needs of a community when a disaster happens. During a disaster, specifically, the response, when the local community is overwhelmed they turn to the state.
When local governments are overwhelmed, the governor can declare a state of emergency which opens up state resources. When the state feels that their resources are also overwhelmed they initiate getting help from the federal government. The governor requests a Presidential Disaster Declaration by demonstrating to FEMA, and others, that the need in their community is so great federal resources are required. From then on, the primary function of the state level government is to act as an intermediary between local and federal government.
The job of the president is to declare a Presidential Disaster Declaration (PDD) at the request of governors and under the recommendation of FEMA. This opens up a world of federal resources to help the impacted communities. PDD's are given when there is a serious need. The federal government looks to other programs within the federal government for assistance before declaring.
During non-response times federal agencies can fund projects that affect emergency management. For example, communities can apply for grants to fund disaster mitigation projects in their communities. The federal government also sets policies that influence emergency management. One obvious example is the National Flood Insurance Program.
It is intended that there be a back and forth between these three entities. The local government knows their constituencies and know the needs of their community but state/ federal can offer resources and expertise that are valuable.
Nonprofits & Grassroots Groups
Nonprofits address the needs that government doesn't. The types and numbers of nonprofits that are involved in emergency management will vary depending on the phase (mitigation, preparedness, response, and recovery). The first nonprofit you probably think of is the Red Cross. They have a federal charter requiring them to respond to disasters. It's not just the Red Cross though, there are dozens of other national disaster nonprofits that deploy to disasters across the country. In addition to these groups, there are all of the local nonprofits that work in the community day-to-day. These groups often become involved in the response and stay involved throughout the recovery. Even though their mission isn't to do disaster response and recovery they see that their community is in need and find a way to help. We also see that new groups and temporary groups form during and after disaster. Some of these group form during response and then disband, others evolve to address recovery needs, and some form only during the recovery.
Nonprofits can also be involved in preparedness and mitigation efforts. Groups that protest Superfund sites or building hazardous pipelines can be thought of along these lines.
Sometimes nonprofits will coordinate with one another and with government officials but for the most part, these groups operate independently.
Individuals and Households
It is better to think of the people who experience a disaster as survivors rather than victims. Survivors are rarely helpless. In fact, in response, they often act as "first responders". It's likely that if someone rescues you during a disaster that it is a neighbor or family member rather than an official search and rescue team. We see that survivors help one another throughout the response by checking on neighbors, sharing resources, and more. Survivors are often the people who form the unofficial groups I mentioned above.
Survivors are the ones who coordinate their own recovery. They're the ones filling out insurance claims, FEMA paperwork, and navigating the complex process of recovery. Before disasters, the individual actions that people take to prepare themselves and mitigate risk are fundamental to emergency management.
With SO many people involved you can start to see how things can quickly get complicated, why coordination is difficult, and misinformation can spread easily.