The U.S. Supreme Court in recent years has been deciding fewer cases on the merits than it has at any time since the end of the U.S. Civil War.
Yet, the volume of cases eligible for its review in the U.S. Circuit Courts of Appeal, and in state supreme courts, is at a near record high. Likewise, the number of certiorari petitions filed is near record highs.
Also, with thirteen different U.S. Circuit Courts of Appeal, the highest military court, 50 state supreme courts, and the highest local courts of the District of Columbia, Puerto Rico, and a handful of U.S. territories all making decisions independently, and federal law having a much more pervasive influence on civil and criminal matters in the U.S. than in most of the post-Civil War era, the potential for conflicts in interpretations of federal law between the almost 70 highest courts it supervises has never been greater. (The U.S. Supreme Court also has a small original jurisdiction docket, mostly consisting of disputes between U.S. states over water rights, consisting of about 5 cases a year.)
And, the U.S. Supreme Court has more justices, now nine, than it did when it was first formed, and much more staff to deal with those cases and to assist the justices in writing opinions on the merits in the cases before it.
The smaller number of cases from 1792 to 1850 is easy to understand. There were fewer people bringing fewer lawsuits and bing prosecuted for fewer federal crimes, there were fewer state supreme courts, and there were fewer U.S. District Courts, and the federal governments regulatory scope and the scope of its activities relative to state governments and the state courts in that time frame was much smaller. (The U.S. federal government's scope and professionalism expanded dramatically during the U.S. Civil War and again during the New Deal and World War II.)
The drop in the first peak, in the 1890s, is also easily understandable. This is when the U.S. Courts of Appeal were created. Before then, in addition to reviewing final decisions on matters of federal law from state supreme courts, the U.S. Supreme Court was also the only court with appellate jurisdiction over the U.S. District Courts.
But the subsequent peaks and declines in U.S. Supreme Court caseloads are harder to explain.
Why has the number of U.S. Supreme Court decisions declined so steadily in the 20th century and 21st century?
One paper looking at the period from the early 1980s and early 1990s suggested that more cases are taken up when there is ideological homogeneity on the court (which makes some logical sense because four out of nine justices must agree to take up a case on the merits), but this is insufficient to explain the longer term trend, and is disputable and somewhat vague.
A previous answer to a similar question at Politics.SE looking at the 1984-1994 also suggested that it could be related to Congress enacting fewer laws and there is some correlation there. But a large share of the work of the U.S. Supreme Court does not involve statutory interpretation, and a small number of mostly old statutes (e.g. 42 U.S.C. § 1983) dominant the ranks of statutes that are litigated and few of those were recently amended, so the line of causation from rates of Congressional statutes enactments to U.S. Supreme Court merits decisions is not obvious.