Both JSON.stringify and JSON.parse support a second argument. replacer and reviver respectively. With replacer and reviver below it's possible to add support for native Map object, including deeply nested values

function replacer(key, value) {
  if(value instanceof Map) {
    return {
      dataType: 'Map',
      value: Array.from(value.entries()), // or with spread: value: [...value]
    };
  } else {
    return value;
  }
}

function reviver(key, value) {
  if(typeof value === 'object' && value !== null) {
    if (value.dataType === 'Map') {
      return new Map(value.value);
    }
  }
  return value;
}

Usage:

const originalValue = new Map([['a', 1]]);
const str = JSON.stringify(originalValue, replacer);
const newValue = JSON.parse(str, reviver);
console.log(originalValue, newValue);

Deep nesting with combination of Arrays, Objects and Maps

const originalValue = [
  new Map([['a', {
    b: {
      c: new Map([['d', 'text']])
    }
  }]])
];
const str = JSON.stringify(originalValue, replacer);
const newValue = JSON.parse(str, reviver);
console.log(originalValue, newValue);

You can't directly stringify the Map instance as it doesn't have any properties, but you can convert it to an array of tuples:

jsonText = JSON.stringify(Array.from(map.entries()));

For the reverse, use

map = new Map(JSON.parse(jsonText));

You can't.

The keys of a map can be anything, including objects. But JSON syntax only allows strings as keys. So it's impossible in a general case.

My keys are guaranteed to be strings and my values will always be lists

In this case, you can use a plain object. It will have these advantages:

• It will be able to be stringified to JSON.
• It will work on older browsers.
• It might be faster.