The 'core' has become synonymous with the abdominal muscles -- the transversus abdominis and the rectus abdominis. The transversus is the deeper muscle while the rectus is the broad surface muscle that we identify as the abs or the six-pack, from which you need to lose a layer of fat to show. You can feel these muscles when forced to brace them -- when you cough or are expecting a punch in the stomach for example.
The core, however, is more than that. Core muscles are involved in bending, twisting, flexing or the torso and in fact, in most of the very agile and athletic movements that we do from time to time. These muscles are essential to our strength and mobility.
The Core Muscles
The main core muscles are:
- Rectus abdominis
- Transversus abdominis
- Obliques (side muscles) - external and internal
- Erector spinae (back)
- Latissimus dorsi (back)
- Quadratus lumborum (back)
- Multifidus (back)
- Diaphragm (chest)
You will notice varying opinion on which of these muscles is critical for core competency, but in the main, these are the muscles involved in optimum core strength and functionality. Notice heavy involvement of the back muscles as well as the abdominal muscles.
Synonymous with core exercise are truck flexing exercises like crunches, situps and rollouts with wheel or on a stability ball. Now these are fine exercises, but you can get the same effect, and even a more comprehensive core workout with compound, full-body exercises as suggested here.
The deadlift is the classic compound exercise because it hits muscles all over the body, including the legs, abdominals, back, chest, arms, legs and neck - some harder than others, naturally. When you progress to lifting sufficiently heavy weights in the deadlift, you can't help but brace the core muscles as you begin the lift from the floor. This is a key to control and stability of the lift and you must develop strong core - abs and back -- when you diligently practise the deadlift. Repeats in the Romanian Deadlift variation is especially useful.
The squat is mostly known for building big, strong legs, but you can't help bracing the abs and core when squatting. Again, core muscles are crucial to control in the best squat form -- on the way down, and on the way up. You can do back squats, front squats, dumbbell squats, and even hack squats -- an oldie but a goodie.
Olympic Lift Variations
The deadlift and the squat are competition lifts for Powerlifting, and, more or less, elements of the big two Olympic lifts - the clean and jerk and the snatch. Other formative practise lifts and derivatives of Olympic lifts are power cleans, hang cleans, push presses, and thrusters. Work these exercises into your regular workouts and you may never need to do another crunch.
Ultimately, it's fun to do crunches and other targeted abdominal exercises like hanging leg raises and rollouts, and variety in training is always good for longevity of your physical activity. Even so, build standard strength training protocols into your weight training and lifting and you will notice vast progress in your core strength.