Beta-blockers interfere with the body's beta-receptors. In some people, an overactive sympathetic nervous system is a factor in hypertension. High ongoing levels of sympathetic nervous system activity tends to raise the heart rate and increases the secretion of adrenaline and related hormones. Beta-blockers slow the heart rate, lower the secretion of stimulating hormones, and also block the effects of adrenaline. In short, the beta-blockers interfere with the "fight-or-flight" response of the body to stress or panic.
States of high sympathetic nervous system arousal tend to be self-reinforcing. If you are panicked, your heart is liable to race; and a racing heart tends to increase your feelings of panic. If the activity of the sympathetic nervous system is damped down by a beta-blocker, this positive-feedback loop is slowed down. A person may feel stress or fear at the mental level, but if the body fails to respond with an increase in heart rate, sweaty palms, and increased adrenaline, then the stressful thoughts will not result in the upward spiral of increased blood pressure and distress.
The way that beta-blockers interfere with the physical mianifestations of anxiety has made them popular for reasons that have nothing to do with treating cardiovascular disease. Although they are not FDA-approved for use in treating anxiety disorders, beta-blockers have been prescribed for various kinds of psychological problems, and they are especially popular for controlling performance anxiety in professional musicians .
Beta-blockers can be life-saving drugs for people suffering from heart failure or arrhythmias. They are also often prescribed for hypertension alone, even when high blood pressure is found without any accompanying heart discorders. Some doctors have achieved excellent results in controlling hypertension with beta-blockers, and some patients are very happy with the effects: not only do beta-blockers lower their blood pressure, but they lower feelings of anxiety as well--like Valium and a blood-pressure drug rolled into one.
But the side effects of beta-blockers can be severe. Weight gain, impotence, and reduced exercise capacity are frequently reported. Beta-blockers can interfere with sleeping patterns, and in some patients can cause nightmares. Depression, fatigue, and thougths of suicide are not uncommon.
In addition to the rather daunting effects listed above, beta-blockers can interfere with peripheral blood circulation and increase blood sugar levels, both of which can be dangerous, especially to diabetics. In fact, like thiazide diuretics, beta-blockers have been shown to be diabetogenic, causing diabetes in long-term users.  There is reason to believe that the diabetogenic effects are enhanced when beta-blockers and diuretcis are given together, and, unfortunately for the patients, this is very common; indeed, my former doctor had me on both of them.
I didn't stay on my beta-blocker (Atenolol) for long, however. Although I did appreciate the anxiety-lowering effect for the first day or two, it immediately interfered with my sleep, making my rest uneasy and punctuated with terrifying dreams. By the end of my first week I was in a low-level state of despair round the clock, and by the second week I was sitting on the floor of distant rooms of the house where no one could hear me, sobbing. You say I should have told my doctor? Probably, but my mental state was so deteriorated after only two weeks that I couldn't face the prospect of dealing with him; I was sure that he would plunge me into more tests, more drugs, more procedures, and that I would end up even worse off. I thought constatly of suicide, and though I never came near to acting upon those thoughts, thee were moments where if I could have pushed a button and had everything be over I might well have done so.
You aren't supposed to quit beta-blockers cold turkey; you are supposed to taper them off gradually under medical supervision. Quitting suddenly, the pharmaceutical inserts tell you, can be deadly--althoug I suspect this applies to heart patients more than to people taking them for treatment of hypertension. In any case, after three weeks on Atenolol I decided to quit. I saw no downside, since the risk of dying seemed minor compared to the horror of spending another day on that drug.
I felt better by the next day, with only minor crying jags. My blood pressure increased slightly for about two days and then declined. After a week my thinking was clearer and I was more-or-less back to normal. I also discovered that I wasn't alone; there are many reports of deep depression and suicidal thinking from beta-blockers, and one Danish study shows that users of beta-blockers have an increased rate of suicide compared to users of other anti-hypertension drugs . I have to say I'm not surprised.
I'm probably not the person to ask about beta-blockers. Not only did Atenolol drop me into a severe depression, I found attempting to exercise while on Atenolol to be a horrifying experience--your effort increases but your heart refuses to keep up with the body's demands.
I've met other people who tolerate beta-blockers well, and even like them. Given the increased risk of diabetes from taking them long-term, they still seem like a bad bargain to me, but you may feel differently. In any case, be aware that beta-blockers can give you a highly distorted view of reality and even plunge you into a state that any professional would diagnose as a temporary mental illness. That's a hefty price to pay for dropping your blood pressure a few points.
 Tindall, Blair. Better Music Through Chemistry. New York Times, Oct. 17, 2004.
 Bangalore, S., et al. A meta-analysis of 94,492 patients with hypertension treated with beta blockers to determine the risk of new-onset diabetes mellitus. Am J. Cardiol. 2007 Oct 15;100(8):1254-62.
 Sorenson, H.K., et al. Risk of suicide in users of β-adrenoceptor blockers, calcium channel blockers and angiotensin converting enzyme inhibitors. Br J Clin Pharmacol. 2001 September; 52(3): 313–318.