Yes, it's quite frightening that there are millions of people in the world walking around with developing heart disease and have no clue it's happening.
Much depends on the progression and nature of one's heart disease. You may be building plaque in your arteries and not feel any symptoms until the plaque ruptures or closes an artery completely or to a level that it causes cells to be damaged. Then you would feel short of breath, sweat intensely and have chest pain radiating to your arms, back and neck. This is normally a crushing pain or a feeling of pressure. All these are what you would feel after a cardiac event.
If you are developing heart disease the first thing to look for is a decrease in exercise tolerance. You may become more tired easily than in the past or find you can not exercise at the same level as before. You may experience short periods of chest pain called angina that can feel like a heart attack but go away with rest. This is because your heart is not getting enough blood under stress. Also, if your heart disease is more of a form of cardiomyopathy such as LVH or dilation of the heart, you may feel more rhythm issues.
Everyone is different so everyone feels things differently. Unfortunately a heart attack is the first symptom 50% of those with heart disease experience so it is important to have this talk with your doctor.
Jon