If you want washboard abs, get your nutrition locked down. If you want actual core strength, do the exercises below.
Paraphrasing Coach Dan John, washboard abs without core strength is like a brand new tire without any tire pressure. The ability to create internal pressure is hugely important in not only lifting but also in sports performance.
The mindset behind core work is shifting to "anti-core" training. Your core is meant to be stable, not to be moving. It's important to be able to resist motion. So ditch the Russian twists and crunches and start doing these exercises if you want to take your core strength to the next level.
Think about keeping a straight line from your knees to your hips to your shoulders. Keep the back flat and don't let your middle sag downward. To make this movement easier, start by using a stability ball, then move to the ab wheel with a limited range of motion as shown here.
Position your body perpendicular to the cable machine. Have the handle at mid-chest height. Get into a half-kneeling position with your inside knee down. Keep shoulders and hips square and press both hands away from your body. Make sure you do a set facing each direction.
Stir-the-Pot on Ball
Start by holding a low plank on a ball. From there, keeping legs straight and back flat, rotate your arms in a circular motion. Make sure to do a set clockwise and counterclockwise. The bigger the circle, the harder it'll be. A wider stance with your legs will make this easier.
Using a set of floor sliders or a towel on a wooden floor, start in a low plank position with your toes on the sliders. Move your body backwards without compensating the plank position. For a more challenging version, perform in a push-up position or by lifting one foot off the ground.
Pick up two heavy kettlebells or dumbbells and go for a walk. A very strong person would be able to carry their bodyweight (half in each hand) for the length of a football field.