Do they take a singular or plural verb? It depends on the sense, but use singular where possible.

Research groups, companies, universities, countries, governments and all other organisations, teams or collective bodies take a singular when functioning as an entity. But use a plural noun when the sense relates to the members of these collectives acting independently of each other. Above all, avoid drifting from singular to plural in references to, say, a research group. Choose whichever is more appropriate and stick to it. If that leaves you with an awkward sentence rewrite it: using “the researchers” instead of “the team” can sometimes get you out of a mess.

Some examples:

“The police is a fine institution” BUT “The police are currently working on this case”

“The team has been awarded a prize” BUT “The team have been working on this project” (has would also be acceptable in the latter case, depending on your point of view);

“The committee gave its unanimous approval to the plans” BUT “The committee enjoyed biscuits with their tea”

“The family can trace its history back to the middle ages” BUT “Before the recession, my brother’s family were quite well off, but now they are hard up.”

The abstract entities mathematics, physics, statistics, acoustics, economics, politics, etc. always take a singular noun. But when they are preceded by the definite article (or could be) statistics (meaning a set of figures), economics (meaning financial detail), politics (meaning a set of activities or political beliefs), they take a plural noun.

See section 2.g) of the full Style Guide for more information on collective nouns.