You can use Collections.sort as follows:

private static void order(List<Person> persons) {

    Collections.sort(persons, new Comparator() {

        public int compare(Object o1, Object o2) {

            String x1 = ((Person) o1).getName();
            String x2 = ((Person) o2).getName();
            int sComp = x1.compareTo(x2);

            if (sComp != 0) {
               return sComp;
            } 

            Integer x1 = ((Person) o1).getAge();
            Integer x2 = ((Person) o2).getAge();
            return x1.compareTo(x2);
    }});
}

List<Persons> is now sorted by name, then by age.

String.compareTo "Compares two strings lexicographically" - from the docs.

Collections.sort is a static method in the native Collections library. It does the actual sorting, you just need to provide a Comparator which defines how two elements in your list should be compared: this is achieved by providing your own implementation of the compare method.

This is not like Collections.sort() where the parameter reference gets sorted. In this case you just get a sorted stream that you need to collect and assign to another variable eventually:

List result = list.stream().sorted((o1, o2)->o1.getItem().getValue().
                                   compareTo(o2.getItem().getValue())).
                                   collect(Collectors.toList());

You've just missed to assign the result

You can use Comparator for sorting data using streams

//first comparison
Comparator<YourType> comparator = Comparator.comparing(s -> s.intervalType.orderIndex);

//second comparison
comparator = comparator.thenComparing(Comparator.comparing(s-> s.item.amount));

//sorting using stream
result.stream().sorted(comparator).collect(Collectors.toList())

(originally from Ways to sort lists of objects in Java based on multiple fields)

Original working code in this gist

Using Java 8 lambda's (added April 10, 2019)

Java 8 solves this nicely by lambda's (though Guava and Apache Commons might still offer more flexibility):

Collections.sort(reportList, Comparator.comparing(Report::getReportKey)
            .thenComparing(Report::getStudentNumber)
            .thenComparing(Report::getSchool));

Thanks to @gaoagong's answer below.

Note that one advantage here is that the getters are evaluated lazily (eg. getSchool() is only evaluated if relevant).

Messy and convoluted: Sorting by hand

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        int sizeCmp = p1.size.compareTo(p2.size);  
        if (sizeCmp != 0) {  
            return sizeCmp;  
        }  
        int nrOfToppingsCmp = p1.nrOfToppings.compareTo(p2.nrOfToppings);  
        if (nrOfToppingsCmp != 0) {  
            return nrOfToppingsCmp;  
        }  
        return p1.name.compareTo(p2.name);  
    }  
});  

This requires a lot of typing, maintenance and is error prone. The only advantage is that getters are only invoked when relevant.

The reflective way: Sorting with BeanComparator

ComparatorChain chain = new ComparatorChain(Arrays.asList(
   new BeanComparator("size"), 
   new BeanComparator("nrOfToppings"), 
   new BeanComparator("name")));

Collections.sort(pizzas, chain);  

Obviously this is more concise, but even more error prone as you lose your direct reference to the fields by using Strings instead (no typesafety, auto-refactorings). Now if a field is renamed, the compiler won’t even report a problem. Moreover, because this solution uses reflection, the sorting is much slower.

Getting there: Sorting with Google Guava’s ComparisonChain

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        return ComparisonChain.start().compare(p1.size, p2.size).compare(p1.nrOfToppings, p2.nrOfToppings).compare(p1.name, p2.name).result();  
        // or in case the fields can be null:  
        /* 
        return ComparisonChain.start() 
           .compare(p1.size, p2.size, Ordering.natural().nullsLast()) 
           .compare(p1.nrOfToppings, p2.nrOfToppings, Ordering.natural().nullsLast()) 
           .compare(p1.name, p2.name, Ordering.natural().nullsLast()) 
           .result(); 
        */  
    }  
});  

This is much better, but requires some boiler plate code for the most common use case: null-values should be valued less by default. For null-fields, you have to provide an extra directive to Guava what to do in that case. This is a flexible mechanism if you want to do something specific, but often you want the default case (ie. 1, a, b, z, null).

And as noted in the comments below, these getters are all evaluated immediately for each comparison.

Sorting with Apache Commons CompareToBuilder

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        return new CompareToBuilder().append(p1.size, p2.size).append(p1.nrOfToppings, p2.nrOfToppings).append(p1.name, p2.name).toComparison();  
    }  
});  

Like Guava’s ComparisonChain, this library class sorts easily on multiple fields, but also defines default behavior for null values (ie. 1, a, b, z, null). However, you can’t specify anything else either, unless you provide your own Comparator.

Again, as noted in the comments below, these getters are all evaluated immediately for each comparison.

Thus

Ultimately it comes down to flavor and the need for flexibility (Guava’s ComparisonChain) vs. concise code (Apache’s CompareToBuilder).

Bonus method

I found a nice solution that combines multiple comparators in order of priority on CodeReview in a MultiComparator:

class MultiComparator<T> implements Comparator<T> {
    private final List<Comparator<T>> comparators;

    public MultiComparator(List<Comparator<? super T>> comparators) {
        this.comparators = comparators;
    }

    public MultiComparator(Comparator<? super T>... comparators) {
        this(Arrays.asList(comparators));
    }

    public int compare(T o1, T o2) {
        for (Comparator<T> c : comparators) {
            int result = c.compare(o1, o2);
            if (result != 0) {
                return result;
            }
        }
        return 0;
    }

    public static <T> void sort(List<T> list, Comparator<? super T>... comparators) {
        Collections.sort(list, new MultiComparator<T>(comparators));
    }
}

Ofcourse Apache Commons Collections has a util for this already:

ComparatorUtils.chainedComparator(comparatorCollection)

Collections.sort(list, ComparatorUtils.chainedComparator(comparators));