What are the most important Collectors and how do you write custom ones?

Collectors define how a terminal collect() operation assembles the stream elements. java.util.stream.Collectors provides ~40 factory methods; the most frequently used in interviews are:

import static java.util.stream.Collectors.*;

// Grouping
Map> byCity =
    people.stream().collect(groupingBy(Person::city));

// Grouping with downstream collector
Map countByCity =
    people.stream().collect(groupingBy(Person::city, counting()));

Map avgAgeByCity =
    people.stream().collect(groupingBy(Person::city, averagingInt(Person::age)));

// Partitioning — splits into true/false map
Map> adultMap =
    people.stream().collect(partitioningBy(p -> p.age() >= 18));

// Joining
String csv = names.stream().collect(joining(", ", "[", "]"));
// e.g. "[Alice, Bob, Carol]"

// toMap
Map byId = people.stream()
    .collect(toMap(Person::id, p -> p,
                   (existing, duplicate) -> existing)); // merge fn for duplicates

// teeing (Java 12) — two simultaneous collectors
record MinMax(int min, int max) {}
MinMax mm = IntStream.of(3, 1, 4, 1, 5, 9)
    .boxed()
    .collect(teeing(
        minBy(Comparator.naturalOrder()),
        maxBy(Comparator.naturalOrder()),
        (min, max) -> new MinMax(min.get(), max.get())
    ));

// toUnmodifiableList/Set/Map — Java 10
List immutable = stream.collect(toUnmodifiableList());