How was Reaganomics supposed to work? What did it actually do? Why is it still relevant today?

Reaganomics was the term given to a set of policies in which tax laws and other measures were designed specifically to favor the wealthy, purportedly as a means of bolstering the economy as a whole and increasing the wealth and standard of living of all classes of society. This, arguably, is the philosophy by which the US and all capitalist countries had always been governed, but a kind of new life was given to it in 1980 when Reagan presented his economic agenda during his presidential campaign. Interestingly, his initial rival for the nomination—but later running mate and vice president—George H.W. Bush at first denounced the plan as "voodoo economics." Reagan's agenda was spearheaded by his economic adviser David Stockman, and gave rise to the description "trickle-down theory," meaning that if the wealthy became wealthier, their wealth would theoretically trickle down to enrich the entire country by stimulating job growth and the higher standard of living that technology creates when businesses do not have any governmental "restraints" imposed upon them. Conservatives vociferously alleged that such restraints had hindered the US in the "mixed economy" existing ever since the New Deal of the 1930s and the "socialist" measures said to have been initiated by Franklin D. Roosevelt.
There is no definitive answer to whether or not Reaganomics "worked." For the first two years of Reagan's administration the country was in a recession which seemed, to many people, to invalidate Reaganomics entirely. After this, however, and for the rest of Reagan's two terms in office, there was a major recovery and the economy started "humming" in a way it had not done for a long time. Reagan's supporters claimed that his policies had been completely vindicated and proven correct. The opposite view was that the success of the economy was merely coincidence, for the US had been due to have an upturn in its cyclical economy anyway, and the technology boom of the 1980s created a huge number of new jobs in the computer field and related areas. Yet, whatever one thinks of Reagan's economic and political goals, he apparently infused a naive sort of confidence in the American people, and rode the waves of a backlash against the supposed failures of liberalism. Reaganomics as a concept is still of importance today, in my view, because it appears to be standard for the Republican Party and the conservative movement to "believe in it" wholeheartedly, in contrast to the skepticism of people such as George Bush, Sr. forty years ago. From the viewpoint of progressives, this is all the more unfortunate because it indicates that the country's shift to the right beginning with Reagan has not yet run its course, in spite of the fact that two of the past three Republican presidential victories (in 2000 and 2016) were actually popular wins for the Democrats in spite of being electoral losses for them.