We investigate the emergence of spanning structures in sparse pseudo-random kuniform hypergraphs, using the following comparatively weak notion of pseudo-randomness. A k-uniform hypergraph H on n vertices is called (p, α, ε)-pseudo-random if for all (not necessarily disjoint) vertex subsets A1, . . . , A k ⊆V (H) with |A1| · · · |A k |≥αn k we have e(A1, . . . , A k ) = (1 ± ε)p|A1| · · · |A k |.For any linear k-uniform F we provide a bound on α = α(n) in terms of p = p(n) and F , such that (under natural divisibility assumptions on n) any k-uniform p, α, o(1) -pseudo-random n-vertex hypergraph H with a mild minimum vertex degree condition contains an F -factor. The approach also enables us to establish the existence of loose Hamilton cycles in sufficiently pseudo-random hypergraphs and all results imply corresponding bounds for stronger notions of hypergraph pseudorandomness such as jumbledness or large spectral gap.As a consequence, p, α, o(1) -pseudo-random k-graphs as above contain: (i) a perfect matching if α = o(p k ) and (ii) a loose Hamilton cycle if α = o(p k−1 ). This extends the works of Lenz-Mubayi, and Lenz-Mubayi-Mycroft who studied the analogous problems in the dense setting.mal since any graph with edge density, say, p < 0.99 satisfies β = Ω( √ pn) (this follows from the proof of [15], see also [29]). /1, project ID: 390685689). 1 Throughout the paper we write x = y ± z to denote that y − z ≤ x ≤ y + z.1 One topic of great importance and popularity in the area concerns the appearance of certain subgraphs F in sufficiently pseudo-random graphs G. Here, F can be a small, fixed size graph such as a triangle, an odd cycle or a fixed size clique, or it can be a large, indeed spanning subgraph of G such as a perfect matching, a Hamilton cycle, or a K r -factor 2 . The fundamental question then concerns the degree of pseudo-randomness which ensures that F is a subgraph of G and we distinguish here the (dense) quasi-random case, when p = Ω(1) and β = o(n), and the (sparse) pseudo-random case, when p = o(1) and β = β(n, p) is a function of n and p. For the quasi-random case the subgraph containment problem is well understood [11,28]; for the pseudo-random case, however, it turned out to be notoriously difficult already for small graphs F , and even more so for spanning subgraphs. Thus, while bounds exist for many classes of graphs F (see e.g. [3]), only few are known to be (essentially) best possible: triangles, odd cycles, perfect matchings, Hamilton cycles and triangle-factors [4,5,29,38].(Linear) pseudo-random hypergraphs. In this paper we investigate the corresponding question for hypergraphs. A k-uniform hypergraph, k-graph for short, is a pair H = (V, E) with a vertex set V = V (H) and an edge set E = E(H)⊆ V k , where V k denotes the set of all k-element subsets of V . Launched by Chung and Graham [12] the investigation of pseudo-random k-graphs is widely popular, albeit mostly restricted to the dense case [1, 8-10, 13, 20, 21, 26, 27, 32, 33, 40-42, 47]. There are several generalisations of (1.1) t...