Most students applying to the College of Engineering (the home of the CS department's biggest major) apply directly to the major. This fall, U. Illinois received more than 4000 applications for Fall 2016 admission to our computer science major. That's significantly more than any other department in the history of the university (beating the previous record of 3200, which was for Fall 2015 admission to CS), almost as much as the total for next two engineering departments (ECE and MechSE) combined, and more than twice as many as we got just three years ago.
Meanwhile, both the average GPA and average ACT scores of CS applicants has been steadily rising; both are significantly higher than the overall average for the College of Engineering (ranked #5 in the country). We're not just getting more applicants; we're also getting better applicants.
Although the number of international applicants has dramatically increased over the last few years, these increases in quantity and quality persist even among domestic applicants, and even among Illinois resident applicants.
The number of new students we admit is also going up, but at nowhere near the same rate. (Roughly 300 this fall, compared to roughly 250 three years ago.) We also admit a small number of transfer students, either from other majors or from the pool of undeclared SOPhomores, but transfers are even more competitive than direct admission.
The number of faculty in the department is also going up, but very slowly—hiring new faculty is a slow and expensive process. And our building isn't growing at all.
So, yeah, CS at Illinois is extremely selective.
But this explosive growth is in no way unique to Illinois. Computer science is becoming more popular everywhere. As a result, admission to computer science has become more competitive everywhere.