We present large-scale 9' × 27' (~25 pc × 70 pc) far-IR observations around Sgr B2 using the Long-Wavelength Spectrometer (LWS) on board the Infrared Space Observatory (ISO). The spectra are dominated by the strong continuum emission of dust, the widespread molecular absorption of light hydrides (OH, CH, and H₂O), and the fine-structure lines of [N II], [N III], [O III], [C II], and [O I]. The widespread dust emission is reproduced by a cold component (T_d 13-22 K) together with a warm component (T_d 24-38 K), representing 10% of the dust opacity. The fine-structure line emission reveals a very extended component of ionized gas. The [O III] 52 μm/88 μm and [N III] 57 μm/[N II] 122 μm line intensity ratios show that the ionized gas has an average electron density of ~240 cm^-3. The ionizing radiation can be characterized by a hard but diluted continuum, with effective temperatures of ~36,000 K and a Lyman continuum photon flux of ~10^50.4 s^-1. The spatial distribution of the ionizing sources with respect to the extended cloud and the clumpiness of the medium determine the large-scale effects of the radiation. Photodissociation regions (PDRs) can be numerous at the interface of the ionized and neutral gas. The analysis of the [C II] 158 μm and [O I] 63 and 145 μm lines indicates a far-UV radiation field of G₀ 10³-10⁴ and a density of n_H = 10³-10⁴ cm^-3 in these PDRs. The widespread OH lines are reproduced by nonlocal radiative transfer models for clouds of moderate volume density (n 10³-10⁴ cm^-3) at T_k 40-100 K. PDR models can explain the enhanced column density of species such as H₂O, OH, and O⁰. However, they fail to reproduce the observed NH₃/NH₂/NH 100/10/1 abundance ratios. For N-bearing species, it seems that shock chemistry has to be invoked. The molecular richness in the outer layers of Sgr B2 is probed by the ISO/LWS Fabry-Pérot (~35 km s^-1) detections toward Sgr B2(M), where more than 70 lines from 15 molecular and atomic species are observed at high signal-to-noise ratios.