In this dissertation, we will discuss Wormald s differential equations method, which has recently had many intriguing applications in Combinatorics. This method explores the interplay between discrete and continuous mathematics and it can be used to prove concentration in a number of discrete random processes. In particular, we will discuss the H-free process and the random greedy algorithm to obtain independent sets in hypergraphs. These processes had been extensively studied through the past few years, culminating in the recent breakthrough of Tom Bohman and Patrick Bennett in 2016, who obtained a lower bound for hypergraphs with certain density conditions. We not only reproduce the proof given by them but also obtain a stronger result (expanding their result to sparser hypergraphs) and we analyze the case of linear hypergraphs, in order to make progress towards a conjecture by Johnson and Pinto concerning the Q2-free process in the hypercube Qd.