A Scrum team in a Scrum environment does not include any of the traditional software engineering roles such as programmer, designer, tester or architect. Everyone on the project works together to complete the set of work they have collectively committed to complete within a sprint. Because of this, Scrum teams develop a deep form of camaraderie and a feeling that "we're all in this together."
Former roles in traditional teams often adapt to an agile role that makes them an integral Scrum team member who retains some of the aspects of their prior role, but also adds new traits as well. New roles in a Scrum team are the ScrumMaster or product owner. You can find out more about which role in a Scrum team would suit you here by finding your pre-agile role.
A typical Scrum team is five to nine people. Rather than scaling by having a large team, Scrum projects scale through having teams of teams. In this way, we have worked on projects with more than 500 people and have consulted on projects with more than 1,000.
Although it's not the only thing necessary to scale Scrum, one well-known technique is the use of a "Scrum of Scrums" meeting. With this approach, each Scrum team proceeds as normal, but each team identifies one person who attends the Scrum of Scrums meeting to coordinate the work of multiple Scrum teams. These meetings are analogous to the daily Scrum meeting, but do not necessarily happen every day. In many organizations, having a Scrum of Scrums meeting two or three times a week is sufficient.
The illustration below shows how a Scrum of Scrums approach allows Scrum to scale up (in this case to 243 people). Each cell represents one person on a Scrum team. The bottom of this illustration shows teams with nine developers on them. One person from each team (the differently colored cell) also participates in a Scrum of Scrum to coordinate work above that team. Then from those nine-person teams, another person is selected (this time shown with diagonal lines) to participate in what is called a Scrum of Scrums of Scrums.
Read more about conducting the Scrum of Scrums meeting.