Direct to the point. Since now I've looked a lot of presentations of $\infty$-categories, but it seems that the only way to do explicit computations on these objects is via model categories. Is that so, or maybe there are other way of doing computations in $\infty$-categories, and if there such different ways what are they?
Edit: I really want to thank all people that answered this question, unfortunately I can choose just one answer. Btw because here is yet midnight I wish everybody a happy new year.