By connecting to port 80 on logsene-receiver.sematext.com (or 443, if you want HTTPS), you can use the Elasticsearch API to search through your data, in the same way you can send it.
Logsene comes with its own UI, which integrates nicely with other Sematext apps, such as SPM (see pub-SPM Wiki). You can also use Kibana. Or deploy your own UI or custom scripts.
Besides web UI, there's also Logsene CLI, a command line interface for searching through logs, with the ability to pipe the output to awk, sed, cut, sort and other useful shell commands. See Logsene CLI Introduction.
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Documentation moved to http://sematext.com/docs/logs/searching-your-events/