How did the Supreme Court get the power of judicial review?
The Supreme Court received this power after the famous Marbury vs. Madison case in 1803. Accordingly, James Madison (Thomas Jefferson's Secretary of State) refused to seat William Marbury as a District of Columbia justice of the peace. The Supreme Court ruled that it was wrong of Jefferson to use his executive authority to prevent the seating of a judge. Marbury had actually been appointed by John Adams, the previous president. His nomination was approved by the senate during Adam's tenure as president. However, James Madison, the new secretary of state, refused to deliver Marbury's commission. Without the commission, Marbury could not be seated.
Unfortunately, although the court ruled that it was wrong not to seat Marbury, it also ruled that it had no jurisdiction over the executive office of president and could not force Jefferson to seat Marbury.
Does the US Constitution specifically designate the power of judicial review to the Supreme Court?
No, it does not.
How can one request the Supreme Court accept and review a legal case?
Anyone who is unsatisfied with the decisions of a lower court may petition the Supreme Court for a review. To request a review, petitioners must ask the Supreme Court to grant a writ of certiorari. Once this is done, the Supreme Court can decide whether it will order a lower court to send up a record of the court case. Note that the Supreme Court is under no obligation to review legal cases that have already been tried in appellate courts.
To accept a case, 4 of the 9 justices must vote to hear the case. However,...
when a request for a stay of execution is made, 5 of the 9 justices must vote to grant a stay. In special circumstances, one Supreme Court justice may grant a stay, but the decision will subsequently be reviewed by the entire court.
How does the Supreme Court decide which cases to accept for review?
The Supreme Court can accept or reject any case. However, it is more inclined to hear cases that have a national impact or that could set an important precedent. An example would be Obergefell vs. Hodges, when the Supreme Court voted to reverse the Sixth Circuit's decision. The 5-4 Supreme Court decision made same-sex marriage legal in all 50 states. Justice Anthony Kennedy wrote for the majority.
What does it mean to "have standing" in a legal case?
Legal standing or locus standi means that the petitioner has the right to bring his/her suit to court. The petitioner has to show that he/she has sustained harm/injury or may sustain future harm from the defendant's actions.
What happens if the Supreme Court’s decision results in a tie?
In the case of a tie, the decision of a lower court is upheld.
Which national issue/debate do you think the US Supreme Court needs to review in the near future?
This will depend upon events of import to our country. Below, I provide two links that list granted Supreme Court cases for the 2018-2019 term.