In the Northern Hemisphere, if you're in the American travel industry, then summer begins this weekend. Victoria Day, a few days earlier, starts the travel-industry summer in Canada. The calendar usually starts summer with the summer solstice, which takes place at 1226 GMT (5:26 am PDT) on June 21. Meteorological summer, approximately coinciding with the travel industry's version, begins on June 1 and ends on August 31.
In most of the country, the warmest weather will be seen in July. The low deserts of the Southwest see their temperatures max out in June in anticipation of the wet phase of the monsoon. (Interestingly enough, the hottest temperatures in parts of Mexico, much of northern and western India and Pakistan correspond with the weeks before the local wet phase of the monsoon as well). I think interior Alaska also sees its max in June, with persistent cloudiness in July and August, combined with decreasing sunshine, serving to lower temperatures.
Hurricane season in the Atlantic Basin starts on June 1 as well, and it's not likely that any tropical storms will jump the gun. The bad news is that NOAA is predicting 13-16 named storms, 8-10 of them hurricanes, 4-6 of them major hurricanes for the upcoming season.
Today's weather is not particularly interesting. The heatwave will continue over the Midwest; widespread temperatures in the 90s can be expected. A slight risk of severe storms is forecast along the I-35 corridor from Oklahoma City to Duluth. Unsettled weather for the Pacific Northwest and northern Rockies (what's new?), sunny and warm for most of California, punishing heat in the lower Colorado Valley and thunderstorms producing heavy rain around the TX/LA border are expected.
Scattered "popcorn" thunderstorms are expected over parts of the South. Without strong winds aloft to separate falling rain and rising warm air, storms tend to develop, blossom, then die before reaching severe limits. If they move slowly, though, they can drop heavy rain.
The larger question is when the trough currently over the Rockies will make its move eastward. Unfortunately for some of us baking in the southern Midwest. the answer is "never" -- it will move northeastward, moderating the northern Plains and Midwest yet letting us bake for another 2-3 days. One model indicates the heatwave moving east over the Appalachians while the other just shows moderation (mid-80s instead of low 90s).