Apple - Where can I find my crash logs?

Open the Console app from the Application -> Utilities, you will see the log files.

Console app has them neatly arranged depending on if a system level process has crashed or a user level process...

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From there you can see if it's in ~/Library/Logs or /Library/Logs - you will get crashes and panics and hangs in separate files. Don't forget to look in /private/var/log as well.

~/Library/Logs/DiagnosticReports/ (where ~ refers to your Home directory).

~/Library/Logs/CrashReporter/MobileDevice are the crashlogs for your iOS devices (if any).

~/Library/Logs/CrashReporter also has links to items in ~/Library/Logs/DiagnosticReports/