React.js, a renowned library for building user interfaces, has evolved dramatically over the years. 

While it simplifies many aspects of front-end development, dealing with asynchronous operations can still be a daunting task for many. 

This guide aims to break down the complexity, focusing on promises, async/await, then, and try/catch within the context of React's functional components.

Let's dive in and decipher these elements in detail.

Promises: Understanding the Basics

A JavaScript Promise represents an operation that hasn't finished yet but is expected to in the future. 

This forms the core of handling asynchronous operations, such as fetching data from a server.

A Promise has three possible states:

• Pending

  : The outcome of the Promise is still unknown, as the operation still needs to be completed.

• Fulfilled

  : The operation has finished, and the Promise has a resulting value.

• Rejected

  : The operation failed, and the Promise was rejected for a reason.

A simple representation of a Promise looks like this:

let promise = new Promise((resolve, reject) => {
  let operationSuccessful = true;

  if (operationSuccessful) {
    resolve("The operation was successful.");
  } else {
    reject("The operation failed.");
  }
});

Promise Handling: Then and Catch

Promises are handled with the .then() method for fulfilled operations and .catch() for rejected ones. 

The beauty lies in the ability to chain these methods due to their Promise return nature.

promise
  .then(message => console.log(message)) // "The operation was successful."
  .catch(message => console.error(message)); // "The operation failed."

Async/Await: A Syntactic Sweetener

While the .then() and .catch() methods do an excellent job of handling Promises, they can lead to convoluted code in more complex scenarios.

That's where async/await comes in, making Promise handling more readable and manageable.

An async function allows us to handle Promises more comfortably. 

Inside this function, the await keyword can be used to pause the execution of the function until a Promise is resolved or rejected.

Error Handling with Try/Catch

When using async/await, we often utilize try/catch blocks for error handling. 

Any errors that occur within the try block will halt further execution in that block and jump to the catch block. This lets us manage errors in a streamlined manner.

Reacting to Promises: Functional Components & Hooks

As React has shifted more towards functional components and hooks, how we handle Promises has also changed. Let's look at how we can integrate Promises with functional components.

Fetching Data Using .then() and .catch()

import React, { useState, useEffect } from 'react';

const MyComponent = () => {
  const [data, setData] = useState(null);
  const [error, setError] = useState(null);

  useEffect(() => {
    fetch('https://api.example.com/data')
      .then(response => response.json())
      .then(data => setData(data))
      .catch(error => setError(error));
  }, []);

  if (error) {
    return <div>Error: {error.message}</div>;
  }

  if (!data) {
    return <div>Loading...</div>;
  }

  return <div>Data: {JSON.stringify(data)}</div>;
}

export default MyComponent;

In the above example, the useEffect hook is used to handle side effects (in this case, fetching data from an API), and the useState hook manages our local state.

The Async/Await Approach

Let's now use async/await to perform the same task:

import React, { useState, useEffect } from 'react';

const MyComponent = () => {
  const [data, setData] = useState(null);
  const [error, setError] = useState(null);

  useEffect(() => {
    const fetchData = async () => {
      try {
        const response = await fetch('https://api.example.com/data');
        const data = await response.json();
        setData(data);
      } catch (error) {
        setError(error);
      }
    };

    fetchData();
  }, []);

  if (error) {
    return <div>Error: {error.message}</div>;
  }

  if (!data) {
    return <div>Loading...</div>;
  }

  return <div>Data: {JSON.stringify(data)}</div>;
}

export default MyComponent;

Here, we've declared an asynchronous function fetchData within useEffect and then called it. We use try/catch for error handling, making the code cleaner and easier to read.

Conclusion

In essence, understanding Promises and async/await is critical to handling asynchronous operations in React. 

This holds even truer with the growing trend of functional components and hooks. 

With the knowledge of these fundamental concepts, you're now equipped to build efficient, data-driven applications using React. 

Remember, mastering asynchronous operations will lead to React applications that are robust, efficient, and provide a great user experience.