Beta-blockers: turning down the adrenaline dial
Beta-blockers sit on the receptors that adrenaline normally activates and quietly occupy them, so the heart hears the stress signal more faintly. The result is a slower [[heart-rate|heart rate]], gentler [[contractility|contraction]], and lower [[card-blood-pressure|blood pressure]] — all of which mean the heart muscle uses less oxygen. That is exactly what you want in angina, after a heart attack, and in many people with heart failure, where calming a chronically over-driven heart actually helps it recover over time.
Because they slow the heart and the AV node, beta-blockers also help control the rate in atrial fibrillation. The same slowing means they are used carefully in people who already have a slow pulse or certain kinds of heart block.
ACE inhibitors and ARBs: blocking the pressure hormone
The body has a powerful pressure-and-fluid hormone system — the renin–angiotensin system. Its end product, angiotensin II, tightens arteries (raising afterload) and tells the kidneys to hold onto salt and water. ACE inhibitors block the enzyme that makes angiotensin II; ARBs block the receptor it acts on. Either way, arteries relax, the kidneys let go of fluid, and pressure falls.
Beyond lowering pressure, this family protects the heart and kidneys over the long term, easing the unhealthy remodelling that follows a heart attack and slowing decline in heart failure and diabetic kidney disease. A common, harmless-but-annoying side effect of ACE inhibitors is a dry cough; switching to an ARB usually resolves it, which is one reason both exist.
Calcium-channel blockers and putting it together
Calcium channel blockers keep calcium out of muscle cells, which makes them relax. There are really two sub-families. One mainly relaxes arteries (the dihydropyridines, names ending in -dipine), lowering pressure and easing angina without much effect on rate. The other mainly slows the heart and AV conduction (verapamil and diltiazem), making them useful for rate control. Knowing which sub-family you mean matters, because they behave quite differently.
Why combine these families in hypertension? Because each attacks pressure by a different mechanism, so two at half-dose often work better with fewer side effects than one at full dose. A very common pairing is an ACE inhibitor (or ARB) with a -dipine calcium channel blocker — one calms the hormone system, the other relaxes the arteries directly.