How to run multiple asynchronous functions then execute callbacks?

Promises give you Promise.all() (this is true for native promises as well as library ones like bluebird’s).

Update: Since Node 8, you can use util.promisify() like you would with Bluebird’s .promisify()

var requestAsync = util.promisify(request); // const util = require('util')
var urls = ['url1', 'url2'];
Promise.all(urls.map(requestAsync)).then(allData => {
    // All data available here in the order of the elements in the array
});

So what you can do (native):

function requestAsync(url) {
    return new Promise(function(resolve, reject) {
        request(url, function(err, res, body) {
            if (err) { return reject(err); }
            return resolve([res, body]);
        });
    });
}
Promise.all([requestAsync('url1'), requestAsync('url2')])
    .then(function(allData) {
        // All data available here in the order it was called.
    });

If you have bluebird, this is even simpler:

var requestAsync = Promise.promisify(request);
var urls = ['url1', 'url2'];
Promise.all(urls.map(requestAsync)).then(allData => {
    // All data available here in the order of the elements in the array
});