Quantum walks are quantum counterparts of random walks. In the first part of this talk, we will define quantum walks and describe the basic results about behaviour of quantum walks in one dimension. We will also describe the two methods to analyze quantum walks: using combinatorial sums and using eigenvector decomposition of a quantum walk. In the second part, we will describe some quantum algorithms that are based on quantum walks. Those algorithms can all be described within one framework, search by a quantum walk. That is, we have a search space in which we search for a solution of some problem. We do that by setting up a quantum walk on the search space that behaves in one way for the solution elements and in a different way for the non-solution elements. If the quantum walk is set up correctly, it may find a solution element quadratically faster than a conventional random walk. The applications include element distinctness (the problem of finding two equal elements in an array) and search on a k-dimensional grid (k>=2).