Node version: 6.10.2
react-leaflet version: 1.1.6
leaflet version: 1.0.3

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@neeraj022 make sure you include the leaflet CSS file and give the map height, <link rel="stylesheet" href="http://cdnjs.cloudflare.com/ajax/libs/leaflet/1.0.3/leaflet.css"> fixed it for me
Thanks...working for me now.. Didn't include leaflet.css in the css file.
How did you fix this @neeraj022 ?
@Roconda you need to add that link rel to your index.html, and also make sure you have this in your index.css:
.leaflet-container {
height: 400px;
width: 100%;
}
I spent the better half of a day trying to figure out what my issue was, @PaulLeCam the instructions need to be clearer to make sure you include the leaflet.css file.
import 'leaflet/dist/leaflet.css';