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I'd suggest placing a @link here. http://stackoverflow.com/questions/10097199/javadoc-see-or-link

I'd suggest placing a @link here. https://stackoverflow.com/questions/10097199/javadoc-see-or-link

private final List<E> peekedElements = new ArrayList<>();
@Override
public boolean hasNext() {
 Optional<E> peekElement = peek();
 return peekElement.isPresent();
}
@Override
public E next() {
 if (!peekedElements.isEmpty()) {
 return peekedElements.remove(0);
 }
 return iterator.next();
}
@Override
public boolean nextMatches(final Predicate<? super E> condition) {
 Objects.requireNonNull(condition, "condition");
 Optional<E> peekElement = peek();
 return (peekElement.isPresent() && condition.test(peekElement.get()));
}
/**
 * Returns an optional containing the next element, or an empty optional if there is none.
 *
 * @return The optional containing the next element, or the empty optional if there is none.
 */
private Optional<E> peek() {
 if (!peekedElements.isEmpty()) {
 return Optional.ofNullable(peekedElements.get(0));
 }
 if (!iterator.hasNext()) {
 return Optional.empty();
 }
 E element = iterator.next();
 peekedElements.add(element);
 return Optional.ofNullable(element);
}

private final List<E> peekedElements = new ArrayList<>();
@Override
public boolean hasNext() {
 Optional<E> peekElement = peek();
 return peekElement.isPresent();
}
@Override
public E next() {
 if (!peekedElements.isEmpty()) {
 return peekedElements.remove(0);
 }
 return iterator.next();
}
@Override
public boolean nextMatches(final Predicate<? super E> condition) {
 Objects.requireNonNull(condition, "condition");
 Optional<E> peekElement = peek();
 return (peekElement.isPresent() && condition.test(peekElement.get()));
}
/**
 * Returns an optional containing the next element, or an empty optional if there is none.
 *
 * @return The optional containing the next element, or the empty optional if there is none.
 */
private Optional<E> peek() {
 if (!peekedElements.isEmpty()) {
 return Optional.ofNullable(peekedElements.get(0));
 }
 if (!iterator.hasNext()) {
 return Optional.empty();
 }
 E element = iterator.next();
 peekedElements.add(element);
 return Optional.ofNullable(element);
}

The Design

A LogReader reads a log, filters the unwanted stuff and converts it into LogEntries. According to your design.

That's a bit much. Split it up.

Make one LogReader that just reads the file and presents you with endless strings. Oh wait, that's a BufferedReader! I'd see the LogReader basically as an iterator wrapper for BufferedReader.

Make a LogParser that takes a Iterable<String> and parses them into LogEntries. Then make a LogFilter that takes a bunch of LogEntries and returns only the ones you want.

Because the input and the output of the LogFilter are the same type, it's now optional for a caller. This simplifies your API when it comes to simple tasks.