The responsible ones

Actors who are responsible for the expansion, for radiation issues and for impact on the environment and on health.

international : ICNIRP (NGO) ; ITU (a UN agency); IRPA  ... and for some reason FCC (a USA-agency) seem to have some international mandate.

And then we have organizations (incl authorities) dealing with impact on health and environment: UNEP ; WHO ; EEA (EU agency).

Most of these actors have been heavily criticized: WHO ; ICNIRP and FCC (see below).

National: A country/nation normally has one authority for each of the segments: Telecommunications grid and permissions; Radiation agency; Health agency; Environment agency.

Regional: Your country may have regional authorities as well.

Local: It may differ from municipality to municipality how these responsibility issues are distributed. Normally there is a possibility in municipalities to write eg. "Citizens' proposal" or "Liability notice" to the municipal board (see What can I do?).

Big players like the EU have a timetable for the introduction of 5G (and most obedient countries follow their schedule). It started around 2016, and most actors aim to have the first part of the 5G network started in 2020. Full introduction globally should have taken place by 2025 according to the EU 5G Action Plan.

Tests have already begun in many cities and universities - especially in Europe: Listed here (but the list is poorly updated). Other advanced areas are USA, China and South Korea.

In USA, the FCC (a heavily criticized authority) makes decisions that also affect internationally.

Sometimes it is difficult to get information from various responsible actors, or laws and regulations have been changed in favor of industries. Following a request to a swedish authority regarding antenna expansion, the following answer was given: "According to PTS's assessment, the information you request relates to the individual's business and operating conditions and is therefore subject to confidentiality pursuant to Chapter 30. Section 23 of the Publicity and Secrecy Act (2009: 400) (OSL). "
Also, some services/techniques may not need permit or license in some countries: Streetlights; antennas that have an older permit; 5G (entirely) and some frequency bands (the Wi-Fi-bands like 60 GHz).
Is this irresponsible & unregulated rollout the reason why insurance companies don't want to insure against injuries from el-smog?  

Often industries, military and universities with suitable equipment are first with the introduction, and they collaborate with telecom companies.  Ericsson presents equipment and 5G challenges.

Facebook* and Google are dominant players in the info-market, and they are not satisfied with just 5G - they want to control it as well. ___* F.ex. the Connectivity project using 60 GHz.

In addition to official installations or test beds, infrastructure is introduced in the rest of society... but often in silence. The street lamps are a good example. In many parts of the world, LED lamps are installed that are adapted for 5G installation (or already have it built in waiting for activation).
5G is being rolled out in this irish municipality dispite its council opposition. 

We need whistleblowers. 

Finally, we must of course mention the part of the infrastructure that the public contributes with: All "smart" products in use have the potential to become a transmitter/receiver in the 5G networks.