representations of p-adic groups and hecke algebras abstract: an explicit understanding of the category of all (smooth, complex) representations of p-adic groups provides an important tool in the construction of an explicit and a categorical local langlands correspondence and also has applications to the study of automorphic forms. the category of representations of p-adic groups decomposes into subcategories, called bernstein blocks, which are indexed by equivalence classes of so called supercuspidal representations of levi subgroups. in this talk, i will give an overview of what we know about an explicit construction of supercuspidal representations and about the structure of the bernstein blocks. in particular, i will discuss a joint project in progress with jeffrey adler, manish mishra and kazuma ohara in which we show that general bernstein blocks are equivalent to much better understood depth-zero bernstein blocks. this is achieved via an isomorphism of hecke algebras and allows to reduce a lot of problems about the (category of) representations of p-adic groups to problems about representations of finite groups of lie type, where answers are often already known or easier to achieve.