Grain boundaries (GBs) can be wetted by a second phase. This phase can be not only liquid (or melted), but it can also be solid. GB wetting can be incomplete (partial) or complete. In the case of incomplete (partial) wetting, the liquid forms in the GB droplets, and the second solid phase forms a chain of (usually lenticular) precipitates. Droplets or precipitates have a non-zero contact angle with the GB. In the case of complete GB wetting, the second phase (liquid or solid) forms in the GB continuous layers between matrix grains. These GB layers completely separate the matrix crystallites from each other. GB wetting by a second solid phase has some important differences from GB wetting by the melt phase. In the latter case, the contact angle always decreases with increasing temperature. If the wetting phase is solid, the contact angle can also increase with increasing temperature. Moreover, the transition from partial to complete wetting can be followed by the opposite transition from complete to partial GB wetting. The GB triple junctions are completely wetted in the broader temperature interval than GBs. Since Phase 2 is also solid, it contains GBs as well. This means that not only can Phase 2 wet the GBs in Phase 1, but the opposite can also occur when Phase 1 can wet the GBs in Phase 2. GB wetting by the second solid phase was observed in the Al-, Mg-, Co-, Ni-, Fe-, Cu-, Zr-, and Ti-based alloys as well as in multicomponent alloys, including high-entropy ones. It can seriously influence various properties of materials.