A system comprising: a cloud provider network including a first control plane service (114A, 118B) to manage customer compute instances hosted on resources (116A, 120B) of the cloud provider network, wherein the resources (116A, 120B) of the cloud provider network include resources deployed within the cloud provider network and resources deployed within a first communications service provider network (200, 302) that is a separate network from the cloud provider network; and a first provider substrate extension (216, 218, 220, 228, 232, 300, 322) of the cloud provider network, wherein the first provider substrate extension (216, 218, 220, 228, 232, 300, 322) includes at least some of the resources deployed within the first communications service provider network (200, 302), and wherein the first provider substrate extension (216, 218, 220, 228, 232, 300, 322): includes a first computer system having capacity for executing customer compute instances; is controlled at least in part by the first control plane service (114A, 118B) via a connection through at least a portion of the first communications service provider network (200, 302), and executes at least a first customer compute instance using the first computer system, wherein the first customer compute instance communicates with a first mobile computer system connected via the first communications service provider network (200, 302), wherein the first mobile computer system is a subscriber to the first communications service provider network (200, 302), and wherein the first customer compute instance communicates with the first mobile computer system without traversing a network that carries traffic of users not subscribed to the first communications service provider network (200, 302). a cloud provider network including a first control plane service (114A, 118B) to manage customer compute instances hosted on resources (116A, 120B) of the cloud provider network, wherein the resources (116A, 120B) of the cloud provider network include resources deployed within the cloud provider network and resources deployed within a first communications service provider network (200, 302) that is a separate network from the cloud provider network; and a first provider substrate extension (216, 218, 220, 228, 232, 300, 322) of the cloud provider network, wherein the first provider substrate extension (216, 218, 220, 228, 232, 300, 322) includes at least some of the resources deployed within the first communications service provider network (200, 302), and wherein the first provider substrate extension (216, 218, 220, 228, 232, 300, 322): includes a first computer system having capacity for executing customer compute instances; is controlled at least in part by the first control plane service (114A, 118B) via a connection through at least a portion of the first communications service provider network (200, 302), and executes at least a first customer compute instance using the first computer system, wherein the first customer compute instance communicates with a first mobile computer system connected via the first communications service provider network (200, 302), wherein the first mobile computer system is a subscriber to the first communications service provider network (200, 302), and wherein the first customer compute instance communicates with the first mobile computer system without traversing a network that carries traffic of users not subscribed to the first communications service provider network (200, 302). includes a first computer system having capacity for executing customer compute instances; is controlled at least in part by the first control plane service (114A, 118B) via a connection through at least a portion of the first communications service provider network (200, 302), and executes at least a first customer compute instance using the first computer system, wherein the first customer compute instance communicates with a first mobile computer system connected via the first communications service provider network (200, 302), wherein the first mobile computer system is a subscriber to the first communications service provider network (200, 302), and wherein the first customer compute instance communicates with the first mobile computer system without traversing a network that carries traffic of users not subscribed to the first communications service provider network (200, 302).