Handling high volume inbound SMS and webhooks with Twilio Functions and Amazon SQS requires offloading incoming requests to a queue, allowing for efficient processing and cost-effective compute resources. By using Twilio Functions, developers can push incoming messages and status callback events onto SQS queues, which can then be processed by background workers at a controlled rate. This approach frees up web applications from handling webhook requests, reduces costs, and enables more efficient message reply logic. The solution is particularly useful for nonprofits and social enterprises that rely on Twilio's communication technology to increase their impact.