Where PNG came from
PNG was designed in 1996 as a patent-free replacement for GIF, after Unisys began enforcing its patent on GIF's LZW compression. It brought lossless compression, 8-bit alpha transparency and 16-bit colour depth, and became the standard format for screenshots, logos, UI assets and anything with sharp edges or flat colour. Its one weakness is photographs: lossless compression handles continuous-tone detail badly, which is exactly the gap WebP's lossy mode fills.
The technical picture
Compression: Lossless DEFLATE. Transparency: Full 8-bit alpha. Animation: Not supported (APNG is a separate extension). Colour: 8-bit and 16-bit per channel, plus palette modes. Typical file size relative to WebP: typically 25-35% larger than lossless WebP, and several times larger than lossy WebP.
Where it opens
Universal since the late 1990s. This is usually the deciding factor when choosing between PNG and WebP — WebP renders in every browser but is uneven in desktop software, while PNG has a very different support profile.
Converting PNG to WebP
Lossless WebP beats PNG by roughly 26% on the same image with identical pixels and identical transparency — a free saving on logos, icons and UI sprites. For screenshots and flat illustrations where a little loss is acceptable, lossy WebP with alpha cuts far deeper than that. If the source PNG is a photograph rather than a graphic, choose lossy WebP — lossless mode will save far less than you expect on continuous-tone detail.
Converting WebP to PNG
PNG is the safe landing spot when you need the image to keep its transparency and open in absolutely everything. Design tools, older Photoshop versions, Office, email clients and CMS uploaders all take PNG without argument, and unlike JPG it will not flatten an alpha channel onto a white box. Expect the PNG output to be typically 25-35% larger than lossless WebP, and several times larger than lossy WebP — that difference is the price of getting a format the destination will actually accept.